Pat the chicken pieces dry and season with the 1/4 teaspoon salt.
Heat 1 tablespoon butter in a large skillet over medium-high heat until melted.
Add the chicken to the skillet and cook, stirring often, until cooked through and no longer pink in the center, about 5 minutes; transfer chicken to a plate and set aside.
Add a second tablespoon of butter to the skillet. Add the sliced red onion and the zucchini/yellow squash and sauté, stirring often, until the vegetables are tender, about 3–4 minutes.
Add the halved grape tomatoes and the cooked chicken back to the skillet.
Stir in the remaining 2 tablespoons butter and cook just until everything is heated through, about 1–2 minutes.
Remove from heat and garnish with chopped parsley or basil if using, then serve.