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 bag or shallow dish and pour the marinade over the chicken, coating evenly.
Refrigerate the chicken in the marinade for at least 1 hour or up to overnight.
Preheat your grill or cast iron grill pan to medium-high heat.
Remove chicken from the marinade and place on the grill; discard leftover marinade.
Grill the chicken 12 to 15 minutes, turning as needed, until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Transfer the chicken to a plate and let rest a few minutes before serving.