In further study, there is a part of Luke in which the grammar used is rather elementrary, suggesting that it was originally written by someone who wrote in Aremaic. Now, we know that Paul contributed with Luke to both Luke and Acts; however, it would be assumed that Paul would have exellent Greek. This suggests that Luke (or whoever wrote this section) would have been Hebrew, or that they at least spoke Aremaic primarily.
The majority of evidence, however, points to Luke being Greek.
