In a bowl, whisk together the Italian dressing, ranch dressing, and BBQ sauce until well combined.
Place the chicken breasts in a large resealable plastic bag and pour the marinade over them. Seal the bag, ensuring the chicken is well-coated with the marinade. Refrigerate for several hours to overnight, turning the bag occasionally.
Preheat the grill to medium-high heat. Remove the chicken from the marinade, discarding the excess marinade.
Grill the chicken for about 15-18 minutes, turning occasionally, until the chicken is thoroughly cooked and has nice grill marks.