Preheat oven to 400 degrees F. Melt 1 tablespoon butter in a large skillet over medium-high heat. Add chicken to the pan; cook, stirring occasionally, until well browned, about 8 minutes. Transfer the chicken to a medium bowl. Add zucchini and bell pepper to the pan; cook, stirring occasionally, until the vegetables start to soften, about 4 minutes. Transfer the zucchini mixture to the bowl with the chicken.