The Greek is Χίμαιρα (chi, stressed iota, mu, diphthong of alpha and iota, rho, alpha). So if I remember the pheonetics of Greek (close enough to Latin), the proper pronounciation should be Kye-me-rah, similiar to what Buff posted.
(The transition between 'me' and 'rah' is soft. 'αι' should be a falling diphthong, the way 'eye' is in English.)