The Ancient Greek noun ἰατρός 'healer' (as in English words like 'psychiatry') and the prefix ἀρχι- 'first' (as in 'archbishop') combined to form ἀρχιατρός, an official role of 'first physician'.

Put ἀρχιατρός through a few centuries of sound changes, and you get the German word for 'doctor', Arzt.