We say “a unique” and not “an unique” because of the “u” sound at the beginning of unique sounds like a “y”. We use the article “a” before consonant sounds.
This is a unique opportunity to buy the company.
This will be a unique experience. I promise.
My name is Aloysius. I think is a unique name.
Why we say A Unique and not An Unique
We use “a” before words that have a “y” sound and “an” before words that don’t have a “y” sound when the word starts with “u”
“A” and “An” are called indefinite articles and usually follow the rule of “a” before words that start with consonants and “an” with words that start with “vowels”. That isn’t always the case when some letters have different sounds.
The two most common letters that are exceptions are “h” which is sometimes silent and therefore the word could start with the second letter and “u” which sometimes sounds like a “y” when it is pronounced.
If you need to decide whether to use “a” or “an” before a word beginning with “u” the best thing you can do is to say the word out loud and decide if it has a “y” sound at the beginning like “A University”.