Donnchad mac Gillai Brigte (or alternatively, Duncan FitzGilbert) (d. 1250) was the first Mormaer or "Earl" of Carrick.

In 1176, he was handed over by his father Gilla Brigte to King Henry II of England as a hostage, to ensure the good behaviour of the former. After his father's death, his cousin Lochlann seized his lands. Henry II tried to intervene on Donnchad's behalf, but Henry II was occupied with the revolts of his sons in France, and moreover, Lochlann had the support of King William of Scotland. As things transpired, Lochlann was allowed to keep most of Galloway. In compensation, a new Mormaerdom was created in the territory of Carrick, which had previously been acquired by the Lordship.

Donnchad had a close alliance with the remarkable Anglo-Norman adventurer John de Courcy. The man who effectively founded the Earldom of Ulster had promised Donnchad lands in Ulster. In 1197 Donnchad himself went to Ulster to secure his lands. John de Courcy was defeated by Hugh de Lacy, but Donnchad nevertheless pursued his claims. When Hugh de Lacy earned the ire of King John of England, many of the supporters of the former fled to Carrick, where Donnchad dutifully arrested them and handed them over.

Donnchad married Avelina Stewart. He had at least 5 sons:
• Níall
• Cuilén
• Eoin
• Alan
• Alexander

Among Donnchad's many descendents is King Robert I of Scotland, who was his great-grandson, through Níall.