Humans show a population-level preference for using the right hand. The fighting hypothesis is an influential theory that suggests that left-handedness persists because its rarity provides a surprise advantage in fighting interactions, and that left-handedness is less frequent because it has a health cost. However, evidence for the health cost of left-handedness is unsubstantiated, leaving the greater frequency of right-handers unexplained. Research indicates that homicide may have been common in early hominins. We propose that the hand used to hold a weapon by early hominins could have influenced the outcome of a fight, due to the location of the heart and aorta. A left-handed unilateral grip exposes the more vulnerable left hemithorax towards an opponent, whereas a right-hand unilateral grip exposes the less vulnerable right hemithorax. Consequently, right-handed early ancestors, with a preference for using the right forelimb in combat, may have had a lower risk of a mortal wound, and a fighting advantage. This would explain their greater frequency. In accordance with the original fighting hypothesis, we also suggest that left-handed fighters have a surprise advantage when they are rare, explaining their persistence. We discuss evidence for the modified fighting hypothesis, its predictions, and ways to test the theory.