Written, hierarchy has four syllables: hi-er-ar-chy. Cambridge gives three: HY-rar-kee in American English and HIRE-ah-kee in British English, where the first part sounds like the word hire. Oxford also lists a four-syllable American form, HY-uh-rar-kee. All of these are correct.
The word is Greek: hierarkhia, the rule of a high priest, from hieros, holy, and arkhein, to rule. In Greek words the ch is a K sound, as in monarchy, anarchy and chaos.
Medieval English spelled it ierarchie, without the H. Writers added the H back around 1500 to match the Latin hierarchia, and today the H is always said. Begin with high, end like the -archy in monarchy, and keep the stress at the front.