He may very well have written it in Greek because that was the Lingua Franca of the Mediteranian world at the time.
Greek was also the language the common people in Judea read the Scriptures in since they spoke Aramaic rather than Hebrew by that time and the Greek Septuagint was the only official translation authorized by the scribes prior to the life of Christ.
If you are interested in the history of the scriptures up to and after the time of Christ I recommend this paper written by an expert as part of a debate: https://www.dropbox.com/s/rxo3o2jh88iemz0/A_Response_to_Gail_Riplinger_re_The_Art_of_Deceit....pdf?dl=0
Bm