In a large nonstick frypan, melt butter in the oil over medium high heat. Season chicken with half of the salt and half of the pepper and add it to frypan. Cook until lightly browned; about 2 minutes per side. Transfer to large plate or platter and cover to keep warm.
Pour off fat from frypan and add squash, zucchini and tomato. Season with remaining salt and pepper. Cook and stir over medium-high heat until squash is slightly softened; about 3 minutes. Reduce heat and return chicken to frypan. Cover partially. Cook until squash is soft and chicken is white throughout but still juicy; about 5 minutes longer.
Transfer chicken to a platter and cover with foil to keep warm. Raise heat to high. Cook vegetable mixture stirring often until almost all of the liquid has evaporated; about 2 minutes. Arrange vegetables around chicken and serve.