A is used before consonants, an before a vowel sound. A comes before words that begin with a u, but are pronounced as though they began with a y: a union; a useful gadget. An comes before a silent h: an heir; an honour. Some people still use an before h in words from French, where the h was silent: an hotel. This is rather old-fashioned. There is no reason to use an before an h which is sounded.So I guess it's "a hypothesis." But to my ear, it sounds a bit like "a apple." I'm just old-fashioned.
Source: a or an.
Perhaps the frequency of use of the word lends itself to the de-hypostasis (grin) of the h in hypothesis. A physical or biological scientist speaking of his theory is going to be using that word a lot. So H's tend to get dropped as a waste of breath. An-'ypothesis, an-'ypothesis.
Vladimir Horowitz's album "An Historic Return, Horowitz at Carnegie Hall" did get an Emmy.