Heat oil in a large nonstick skillet over medium-high heat. Sprinkle chicken with salt and pepper; add chicken to pan. Cook 4 minutes on each side; remove from pan. Keep warm.
Reduce heat to medium. Add cubed squash and zucchini to pan, and cook 2 minutes, stirring frequently. Return the chicken to pan.
Combine broth and remaining ingredients in a small bowl, stirring with a whisk. Add the broth mixture to pan. Cover, reduce heat to medium-low, and cook 3 minutes.