In a bowl, whisk together 3/4 cup Italian dressing and 3/4 cup thick teriyaki sauce until combined.
Place the 4 boneless skinless chicken breasts in a resealable plastic bag or shallow dish and pour the marinade over them, ensuring the chicken is evenly coated.
Refrigerate the chicken in the marinade for at least 1 hour or up to overnight.
Preheat your grill or a cast iron grill pan over medium-high heat and prepare tools for cooking.
Remove chicken from the marinade, letting excess drip off, and grill 12 to 15 minutes, turning as needed, until the internal temperature reaches 165°F (74°C).
Use a meat thermometer to verify the chicken is fully cooked before serving.