Answer:
It's always "a" when it is before a word that does not start with a letter that is a vowel or sounds like a vowel. Therefore, the correct grammar is "a historical background."
Actually, the above is not entirely correct. It is quite acceptable to use "an" in front of a word beginning with the letter 'h' when the word is not stressed on the first syllable. So, for example, it is quite acceptable to say "an historical background" or "an heroic feat", but it is not correct to say "an heritage".