In a small bowl, combine the soy sauce, sesame oil, minced garlic, and grated ginger. Set aside.
Heat the vegetable oil in a large skillet or wok over medium heat. Add the sliced chicken breasts and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced bell pepper and cook for 2 minutes. Add the torn Swiss chard leaves and cook until wilted, about 3-4 minutes.
Return the cooked chicken to the skillet and pour in the soy sauce mixture. Stir to combine everything well and cook for an additional 2 minutes.
Season with salt and pepper to taste. Serve the stir-fry hot with steamed rice or noodles.
Enjoy!