The answer is "a university" because we depend on the pronounciation of the word not the letter that it begins with. Here the letter "u" is pronouned as "yew" which is written in transcription as /j/.

Use "an" because the word "university" starts with a vowel. If you use a noun with an adjective, choose an article that matches the adjective.

A university. Articles are put before vowels and consonants phonetically - according to the 1st sound but not according to the 1st letter. In "university" the 1st letter is "u" - a vowel but the 1st sound is [j] - a consonant, thus you should use "a".

"A" becomes "an" before vowels because the "n" makes it easier to pronounce. an alphabet an apple an editor an empty glass an incomplete sentence an indirect question an opera an opportunity an unusual event an uncommon word a bag, a cat, a dog, a foot, a game, a hot potato, a job, a kite, a lamp, a map, a name, a pet, a quiz, a room, a seat, a team, a vase, a windy day, a zipper. Yet there are exceptions. As Dr. B and Nada have pointed out, because "university" begins with the SOUND, "yew," the article before it is "a," NOT "an." One would also say, "A universal rule," "A unitary principle" because the pronunciation of "u" is "yew" in both cases. In addition, some words that begin with the letter "h" don't pronounce it. For example, "honor," "herb" (in American English). Because the SOUND is of a vowel (respectively "o" and "e") one should use AN: an honor, an herb. When the "h" is pronounced (happy, hand), then "a" is used: a happy dog, a handful of grass, a hard test. How a word is pronounced guides the use of "a" or "an," NOT the spelling.

The rule is "a" before a vowel sound (not letter) and "an" before a vowel sound. Thus a hospital but an hour an ugly building but a university an only child but a one-legged man an elephant but a European trip