Am I obliged to share my most promising data? I have just started a PhD along with another candidate. We are each looking at different aspects of the same subject. His data provide context for mine, while my data simply add value to his. As I will be asking him for some of his data, he has decided that he wants some of my data.  However, he is interested in using a particular part of my data which I think will be the most fruitful part of my PhD. 

His data are quicker to prepare than mine, and he will undoubtedly write up his chapters/ publications before I get a chance.  I am worried that this will have a negative impact on my ability to publish my papers.  

Do I have to give him my most promising data?  Is there any way around doing this? I would prefer to rely on older data from Honours students looking at this subject and not ask for his data, if this allows me to keep my own data.
What does your supervisor say about this?

I've seen situations where someone not sharing data not only prevented papers being written, but completely obliterated the collaboration. 

One possibility is handing the data over, but helping with its analysis and the subsequent writing of the paper (with co-authorship). You could offer the same to the other candidate.

In any case, as you have only just started, I wouldn't worry about the negative impact. There's plenty of time to build.