In a mixing bowl, combine the 1 cup of Italian dressing and 1 cup of low sodium soy sauce. Use a whisk or spoon to mix until well blended.
Place the boneless skinless chicken breasts in a resealable plastic bag or a shallow dish. Pour the marinade over the chicken, ensuring each piece is well coated. Seal the bag or cover the dish, then refrigerate for at least 1 hour. For best results, marinate for 4 to 8 hours.
If grilling, preheat your grill to medium-high heat. If baking, preheat your oven to 375°F (190°C). For stovetop cooking, heat a skillet over medium heat.
Remove the chicken from the marinade, letting excess liquid drip off. For grilling, cook the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F (75°C). If baking, place the chicken on a baking sheet and bake for 25-30 minutes. For stovetop, cook for 6-8 minutes per side.
Once cooked, remove the chicken from heat and let it rest for about 5 minutes before slicing. This allows the juices to redistribute throughout the meat.