His integrity was questioned over numerous illegal structures built at his home on The Peak.
He has demolished them and apologised, but demonstrations were held on the day he took up the post and many questions remain.
Young Post asked Hong Kong students what they would like to say or ask him, if given the chance.
Here are some of their comments.
Nicole Liang, 15, PLK Choi Kai Yau School
As a leader, integrity is a really important quality. Throughout all the events that have happened, it is sad to see your integrity being questioned and at a low point.
Explaining and admitting your flaws will bring no benefits at this stage.
But, a brief explanation to the public will provide a short-term interval of "peace" - both for society and yourself.
Jolie Lau, 15, HKCCCU Logos Academy
I'm still supporting you wholeheartedly. I believe you'll be a great chief executive of Hong Kong.
Even though I am amazed by how Hongkongers have come together to fight for what they want, I think they're a bit over the top about the integrity issue over the illegal structures.
Maybe it was all just a mistake?
Joshua Wang, 16, Yew Chung International School
We are aligned in our protests and movements. Our demands for democracy are our single desire. All I hope for is a government for the people, driven only by the public's needs, and liberated from redundant politics. That's what we hope for.
Matthew Suen, 16, Queen Elizabeth School
You - an Executive Council convener for many years - denied claims of illegal structures at your home during the election campaign. But the media revealed at least six illegal structures in your house. It has been alleged that you gave false information and tried to deceive the public. If you deliberately lied, then it brings into question whether you can hold such a high office as Chief Executive and govern us for the next five years. The issue is not about whether you built illegal structures, but whether you deliberately fabricated an explanation afterwards.
Howard Yeung, 19, CUHK
I expect you to be a powerful leader: someone with your own vision, who truly has the best interests of Hong Kong at heart and will not be shaken by the tongues of politicians and media - regardless of the great pressure you face in the future.
I expect you to be a commanding, trustworthy leader as you serve the public. We need a leader who dares to bring us real changes in the new era.
Hong Kong cannot rely forever on its past successes and the support of the mainland. So surprise us, but do not disappoint us.
Lorenzo Borje, 17, Renaissance College
How will you work to improve the state of urban development in Hong Kong? As it currently stands, government investment has focused mainly on large-scale infrastructure projects, such as the Hong Kong-Zhuhai-Macau bridge and the Kai Tak site redevelopment. Will there be a more pronounced shift towards promoting innovative schemes that improve Hong Kong’s sustainability as a whole?
Lillian Wat, 18, Wa Ying College
How many passionate voices have you heard from the July 1 demonstrations? Hong Kong people are hoping for democracy, liberty, stability, happiness, and an honest chief executive who is worthy of our respect and trust. Being a decision-maker in the government, please make the right choices for Hong Kong over the next five years and fight for our future - so one day we can enjoy universal suffrage.
Fiona Lee, 16, St Margret’s Girls College
C.Y. Leung, why don’t you just tell the citizens the truth and say sorry?
Macy Ying, 16, Methodist College
How can you balance the views of the different parties and solve the disputes of "cultural differences" and "conflict of interests" between Hong Kong citizens and the mainland Chinese?
Aleena Wong, 17, St Paul’s Convent School
I applaud you for your effort to strengthen your image as a leader who listens to people by frequently holding public forums. But I hope you can try to hold some public forums in English for ethnic minorities so that they too may be able to voice their concerns to you more freely.
Ehab Ebeid, 17, Li Po Chun United World College of Hong Kong
I think you should try to distance yourself from the Beijing government and the Chinese Communist Party. I just think someone from the pan-democracy camp would’ve been a better chief executive.
Karen Lee, 17, Canossa College
C.Y., I supported some of your proposed policies when you were running for election, especially those helping the grassroots to live better. We certainly need to unite with "one heart" for the society and I believed in your promises. However, your integrity is challenged by the recent illegal structure scandal and made me feel a bit worried. I hope your "evolve but maintain stability" spirit doesn’t take away our freedom, and I ask you to respect the "one country, two systems" because that is what Hong Kong people have been fighting for during the past 15 years.
Page Leung, 20, HKU
I hope you can lead our city so there is mutual respect between the government and the people. Freedom of speech and of the press should be upheld by all means. This way, Hong Kong will move forwards not backwards. You have to remember the principle of "one country, two systems" when governing and set a time for universal suffrage.
Timothy Lam, 18, CUHK
I wish you will show your stance on political freedom and on the June 4 incident. Although I agree concentrating on improving the living of the lower classes is important, safeguarding our liberty is also vital for the sustainable development of Hong Kong. All governing issues should be open for discussion to ensure decisions have taken into consideration most aspects.
Alex Chu, 17, St. Joseph’s College
Now the new term of office has started, I want you to review the current education curriculum. The burden is too high for Hong Kong students and many of us have decided to study aboard. This will be detrimental to the entire social system, so and I urge you to seek for a solution towards the situation.
Quentin Yiu, 19, Li Po Chun United World College
After the scandal regarding illegal structures, your integrity has been put in doubt – especially to a teenager who aspires to become an architect. Similar lies can only be detrimental to the reputation of other local professionals. To become a successful Chief Executive, I hope you can realise the difference between Hong Kong and China. Article 23 can only lead us to an abyss.
Cliff Chung, 16, Diocesan Boy’s School
I expect you to act as you promise. You should not run your policies at full speed at the beginning, but do it step by step instead.
Nicole Kit, 19, HKU
You need to help Hong Kong to develop into a sustainable city. How much effort will you put into ecological and environmental protection for Hong Kong?
Vincent Au, 21, HKBU
I sincerely hope that you can face the questions regarding your integrity and your uncertain stances towards the June 4 incident directly.
Coco Lam, 15, Marymount Secondary School
What measures will you take to ensure an equal share of rights among the Lesbian, Gay, Bisexual and Transgender (LGBT) citizens of Hong Kong?
Wong Chung Chun, 16, Tang King Po School
I think your actions have been suspicious and hard to understand. People said you are from the Chinese Communist Party and you said there would be no quota for mainland mothers to deliver babies in Hong Kong. Isn’t this a contradiction if you are really secretly appointed by the China government? What do you want to do?
Becky Yip, 18, Queen Elizabeth School
I’ve supported you since you gave us a talk about cherishing the chance of contributing to our nation some years ago. Being Chief Executive of the HKSAR is a tough job, but I think you can do it well.
I expect you to provide more chances for youngsters to make full use of our abilities and make contributions to Hong Kong and China. I believe in you, C.Y.
Angus Lui, 15, Shatin Tsung Tsin Secondary School
You should immediately resign if it is proved you have lied. We can’t have a liar as our Chief Executive.