I Am an HIV+ Man and I Have Lipodystrophy Under my Arms. Am I a Candidate for Coolsculpting?

I doubt you mean the true underarms or axillae, possibly the fat pads near the underarms. The applicators for CoolSculpting may not fit the underarm areas.I would be concerned about nerve sensitivity and numbness there. It has been used off-label, especially with the new flat applicator on the upper outer arms. You need to be examined in person by a physician to determine if you're a candidate and to discuss the risks with both the arms and chest as they are both off-label. 

Coolsculpting has not received FDA approval to treat fat for under the arms. Proceed with caution as HIV will complicate your healing and may restrict your results.