An hour is correct, because "hour" begins with a vowel sound. A vs. an depends on pronunciation, not spelling.
Some notable cases:
- A/an NIC (network interface card)--proper spelling depends on prounuciation... "A nick" vs. "an N-I-C"
- A/an herb. "An erb" in most regionsmany cases/regions. "a herb" (with pronounced H) in some