Is it Within a hour or within an hour?

Answer 1

An hour. Whether to use "a" or "an" is based on sound. If it is a vowel sound, then use "an." If it is a consonant sound, use "a." Since the *sound* at the beginning of the word "hour" is a vowel sound, we use "an."

You could also state it as an exception:

We use "an" next to a word start with vowels letters like "a, e, i, o, u" and we use "a" to a word starts with consonant letters ( b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z). But the word "hour" starts with a consonant letter. If the word with a consonant letter at the beginning is pronounced with a vowel sound we use "an" instead of "a."

Answer 2

Within an hour.

The "h" is silent you treat it like it starts with a vowel.