The standard rule for a word beginning with a vowel is to use "an".
Wouldn't the word unique be an exception to the rule?
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Not really, because the rule applies to the spoken sound not the written vowel, which in this case is a 'you' sound, so you use a. this is why so many words beginning with an unsounded 'h', for example honest, take the an.
What about the word historic?
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an historic or a historic.
Either way.
what about university? an university or a university?
A university. A uniform. A unilateral declaration. A useful tool.

With 'historic', it depends on how you pronounce it. Brits would say "A historic day" with a hard H. I think Americans would say "An historic day" with a silent H.
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You could say that, generally, where "an" precedes an initial "h", the "h" is either silent, or belongs to an unstressed syllable.

In the latter case, both options ("a" and "an") are often available.

Best wishes,

Hmmmm, I guess that's why unique is "unique". 
A goes before CONSONANT sounds whereas AN goes before VOWEL sounds, this is pretty plain to see. And it also makes easier joining the words as we speak.


a unique, a uniform, a university, a universal problem, a unilateral agreement, a united nation, a once-in-a-lfetime opportunity

an hour, an honest man, an heir

Concerning the word historical, here in Canada most people would go for A Historical as well as in the US. However, I do hear people say AN Historical here in Canada and I think I myself say it like this sometimes, but in this case the letter H is not pronounced. But before HISTORY, always A.
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