Albert Barnes on Acts 21:37

May I speak unto thee? May I have the privilege of making my defence before thee; or of stating the case truly, the cause of my accusation, of this tumult, etc.

Canst thou speak Greek? Implying that if he could, he might be permitted to speak to him. The Greek language was that which was then almost universally spoken, and it is not improbable that it was the native tongue of the chief captain. It is evident that he was not a Roman by birth, for he says, Acts 22:28 that he had obtained the privilege of citizenship by paying a great sum. The language which the Jews spoke was the Syro-Chaldaic; and as he took Paul to be an Egyptian Jew, Acts 21:38, he supposed, from that circumstance also, that he was not able to speak the Greek language.

(*) "chief captain" "Commander"