...was the language of the Jews in 1st century Palestine. I'm not following your logic that Greek would be his first language.
Josephus said (Antiquities 20.21.2): "I have also taken a great deal of pains
to obtain the learning of the Greeks, and understand the Greek language, although I have so long accustomed myself to speak our own tongue [Aramaic], that I cannot pronounce Greek with sufficient exactness; for our nation does not encourage those that learn the languages of many nations..."
As J.P. Meier observes (A Marginal Jew, Vol. I, page 261): "Admittedly, all this sheds at most a very indirect light on our main question, the language that Jesus knew and used best. But if even the gifted Jerusalemite intellectual Josephus was not totally at home in Greek after years of writing in it while living in Rome, and if in AD 70 he had found it necessary or at least advisable to address his fellow Jews in Jerusalem in Aramaic rather than Greek, the chances of a Galilean peasant knowing enough Greek to become a successful teacher and preacher who regularly delivered his discourses in Greek seem slim."
Inscriptions of the time evince that the commonly spoken Aramaic was mostly free of Greek influence on its vocabulary, unlike in later centuries (Meier, page 265). Although they are all written in Greek, the only foreign words that the Gospels put on the lips of Jesus are in Aramaic, such as in Mark 5:41, 7:34, and 15:34. The Greek Gospel of John says that Jesus named Simon as Kephas (Jn 1:42), and Paul used the Aramaic address to God, abba, even when writing to Greek-speaking Gentiles in Gal 4:6 and Rom 8:16.
Meier concludes his discussion with these words: "Jesus regularly and perhaps exclusively taught in Aramaic, his Greek being of a practical, business type, and perhaps rudimentary to boot." (page 268)
http://www.experiencefestival.com/a/historical%20jesus%20-%20what%20language%20did%20jesus%20speak?/id/1467843
During Jesus' lifetime, in the first century CE, Jews in Judaea are believed to have primarily spoken Aramaic with a dwindling number using Hebrew as a native language. Many learned Hebrew as a liturgical language. Additionally, Koine Greek was an international language of the Roman administration and trade, and was widely understood by those in the urban spheres of influence. Latin was spoken in the Roman army, but had almost no impact on the linguistic landscape.
http://en.wikipedia.org/wiki/Aramaic_language#Languages_during_Jesus.27_lifetime
And I don't know if Jesus would have been considered "urban" -- he may have known some Greek, as a tradesman (being a carpenter), but I see no evidence that it would be his first language, or the language he would use to speak to fellow Jews.
Here's another article, if you are interested:
http://en.wikipedia.org/wiki/Aramaic_of_Jesus