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?)
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
In sentence 1, "He had a chance to study in high school again," the phrase "to study in high school again" is an infinitive phrase. It acts as the complement of the noun "chance." So in this sentence, there is no apposition between the "that clause" and "a chance."
In sentence 2, "He had a chance that he could study in high school again," the phrase "that he could study in high school again" is a relative clause. It functions as an adjective that modifies the noun "chance." This relative clause provides additional information about the nature of the chance. Therefore, in this sentence, the "that clause" is indeed in apposition with "a chance."