Form 1095-A reports your insurance premiums and associated advance premium tax credit. The IRS does require you to complete form 8962 if you receive a form 1095-A.

Because you are receiving a form 1095-A, you must be enrolled in an insurance plan through the government exchange. As such, you would be entitled to a premium tax credit if your income was below a certain amount. Also, you would not be allowed to have insurance through your employer.

How is it that you have an insurance plan through the exchange but you don't pay the premiums?

A third party is paying my premiums directly to the insurance company.  That's why I don't think I'm entitled to a credit.

By third party, I assume you mean a friend, relative or associate. If so, it would be looked on as a gift to you and then you turn around and pay the insurance premium. In that scenario, you would be considered to have payed the premium yourself, so you would be entitled to the credit.