Does Greek have an equivalent of “ch” as in “chicken”?

Standard Greek does not. <ch> gets transliterated as /ts/. For example, when I was in Goody’s (the Greek competitor to McDonald’s) and ordered a cheeseburger, my order was relayed as ena tsiz! . You’ll see many Turkish loanwords with /ts/ in them: every single one corresponds to a Turkish <ç>.

On the other hand, many Greek dialects do have a [tʃ] sound, as a palatalised /k/ (which is how the sound originated in English). Confronted with the street name McCutcheon, for example, my mother wrote it down in Greek as <Makakion>. Which, in Cretan dialect, would be pronounced [makatʃon].

Kazantzakis also did something like that in a letter home to his parents from Italy; but I don’t remember what his word was.