In this paper we contribute in this direction presenting the first Greek annotated dataset for offensive language identification: the Offensive Greek Tweet Dataset (OGTD). OGTD uses a working definition of offensive language inspired by the OLID dataset for English (<cite>Zampieri et al., 2019a</cite>) used in the recent OffensEval (SemEval-2019 Task 6) (Zampieri et al., 2019b) .