Chandragupta Maurya married a daughter of his eldest maternal who had come to Pushpapura (Patliputra) with the King’s mother. He wedded her and raised her to the dignity of Queen Consort. She became pregnant and after taking precautions, her pregnancy got to full term.She was mother of Bindusara who died due to eating poisoned food of Chandragupta Maurya when she was just seven days from delivery. Chanakya cut her head off and did cesarion. The baby was kept in bellies of different goats for seven days and due to blood spots on the baby, he was named Bindusara.
Source- Mahavansh Tika (written in 10th Century CE)
Chandragupta had a queen named Durdhara and when she was pregnant, out of deep love for the King, sat to dine with him. The food was mixed with poison by Chanakya to make him immune. As soon as she ate his food, she died immediately. Chanakya to save her child did cesarion and due to a mark of poisoned blood on his forehead, he was named Bindusara.
Source- Parishisth Parvan (written in 12th Century CE)
There is no source available which says Durdhara was a Greek. In both Mahavansh Tika and Parishisth Parvan, she is mentioned as Chief Queen (Queen among all the queens of Chandragupta).