1. He had a chance to study in high school again.

2. He had a chance that he could study in high school again.

(Is the 'that clause' in apposition with 'a chance' in Sentence 2? what about in #1?)

2 answers

I think the noun clause in 2 (that...again) is serving as an appositive for the noun preceding it. In 1, though, the infinitive phrase (to study...) seems to be describing "chance" and is serving as an adjective.
http://www.k12reader.com/term/noun-clause/

and

http://www.chompchomp.com/terms/infinitivephrase.htm