In Irish mythology, Conchobar mac Nessa (also Conchobor, Conchubar, Conchobhar, Conchubhar, Conchúr, Conchúir, Conor) was king of Ulster during the events of the Ulster Cycle. He is supposed to have ruled from Emain Macha (Navan Fort near Armagh) somewhere around the time of Christ.

He was named from his mother, Ness, a warrior princess. His father was either Cathbad, chief druid of Ulster and Ness's husband, or Fachtna Fáthach, High King of Ireland and Ness's lover. Ness tricked Fergus mac Róich out of the kingship of Ulster to give it to her seven-year-old son.

Conchobar was present when Deirdre was born, and heard the prophesy that she would be very beautiful, but would bring war and disaster. He decided to have her brought up in isolation, and when she was of age, marry her, but she eloped with a young warrior called Naoise. The couple fled to Scotland along with Naoise's two brothers, but wherever they ended up the local king would try to have the brothers killed so he could have Deirdre for himself.

Eventually Conchobar tracked them down to a remote island, and sent Fergus mac Róich to them with his guarantee of safe passage home. However Fergus was waylaid, and Conchobar had the brothers killed, forcibly marrying Deirdre. Fergus was outraged at this betrayal of his word, and took his followers (including Conchobar's eldest son, Cormac Cond Longas) into exile in Connacht, where Ailill and Medb took them in. Fergus and his Ulster exiles later took part in Medb's invasion of Ulster in Táin Bó Cúailnge (the Cattle Raid of Cooley).

Conchobar, frustrated by Deirdre's lack of love for him, offered her to Éogan mac Durthacht, who had carried out the murder of Naoise. Deirdre committed suicide.

Conchobar was eventually killed by the Connacht warrior Cet mac Mágach. Cet had stolen one of Ulster's trophies of battle, the petrified brain of Mesgegra, king of Leinster, and shot it from his sling so it embedded itself in Conchobar's head. Conchobor's physicians were unable to remove it, but sewed up the wound and told the king he would survive so long as he didn't get excited or over-exert himself. Seven reasonably peaceful years later, Conchobar was told of the death of Christ, and got so angry that the brain burst from his head, and he died.

Conchobar's nephew was the great Ulster hero, Cú Chulainn.