Cicero

Though it is almost impossible to tell how the ancient Romans would have pronounced something, judging by the fact the Romans were obviously Italian, they probably, as I was informed by my Latin teacher, have pronounced -ce and -ci like modern Italians. That would make this name Chi-che-ro. Though of course, one cannot be certain.

No, the pronunciation provided by the anonymous user (and honungspinglan) would be correct in Classical Latin.

In Latin it would be pronounced ki`kero (long i, short e, long o, emphasis on the first syllable).

At first it was pronounced Kikero. Caesar was pronounced Kajsar. C was pronounced as K and Ae as aj or just as I in English.