Online health support groups are places for people to compare themselves with others and obtain informational and emotional support about their disease. To do so, they generally need to reveal private information about themselves and in many support sites, they can do this in public or private channels. However, we know little about how the publicness of the channels in health support groups influence the amount of self-disclosure people provide. Our work examines the extent members self-disclose in the private and public channels of an online cancer support group. We first built machine learning models to automatically identify the amount of positive and negative self-disclosure in messages exchanged in this community, with adequate validity r>0.70. In contrast to findings from non-health-related sites, our results show that people generally self-disclose more in the public channel than the private one and are especially likely to reveal their negative thoughts and feelings publicly. We discuss theoretical and practical implications of our work.