In a small saucepan over medium-low heat, mix ketchup, fruit, Worcestershire, mustard, and a pinch of salt. Cook for approximately 20 minutes to thicken, stirring often.
Preheat grill or a grill pan to medium-high. Toss chicken with olive oil and a dash of salt.
Grill chicken for 1 to 2 minutes. Turn and brush BBQ sauce on cooked side, cooking for an additional 1 to 2 minutes. Turn again and brush other side with BBQ sauce, cooking 1 to 2 minutes. Turn once more and finish cooking for about 1 to 2 minutes.
