Well yeah let me just reinforce what others have said:
If the word following the "a" or "an" is pronounced starting with a vowel then you use "an", otherwise use "a". Seeing as "unique" is pronounced "yooneek" i.e. starting with a consonant, you use "a".
And pcgiant is right... in the same way you use "the" pronouncing the "e" like the "i" in "dirt" when the next word is pronounced with a consonant and "the" pronounced "thee" when the next word is pronounced starting with a vowel.
Damn I hate long explanations but I feel it is my civic duty