What state in US ends with three vowels?

Hawaii--sort of.

Technically, the name of Hawai'i must be written with an apostrophe between the last two i's. This apostrophe represents the glottal stop, which is a consonant in the Hawai'ian language. Thus, if you use the correct spelling of Hawai'i, then the word ends in a consonant and a vowel (' and i). Because the apostrophe is not used this way in English, most people outside of Hawai'i are unaware of this fact.

In Hawai'i, the name of the state is pronounced huh-VAI-ee, with a clear glottal stop between the two i sounds.