Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Heat olive oil in a skillet over medium heat. Add onion and garlic; sauté until tender, about 2 minutes. Stir in ketchup, honey, brown sugar, apple cider vinegar, Worcestershire sauce, salt, and pepper; simmer until sauce has thickened slightly, about 1 or 2 minutes. Remove from heat; set aside to cool slightly.

Dip chicken in sauce to coat on both sides; reserve remaining sauce in the skillet. Transfer chicken onto the preheated grill and cook, turning once, until nicely browned on all sides, about 10 to 15 minutes.