Steve Shaw is right that it the "famous" pronunciation is "Tie-eece"/Tie-eece." However, the Greek name is Θαις (with diacriticals on the ι, but I don't know the HTML entity for that, and Mudcat isn't reliable on unicode in my experience). Thus the woman of Alexander the Great's time would have pronounced it with a "Th," not a "T" (and an a rather than the ie).

So it's a matter of choice: "Thay-ees" if one wants the Greek way; "Tie-ees" if one wants the operatic way. :-)