Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the chicken pieces and cook, stirring occasionally, until golden brown and cooked through, about 5–7 minutes; season with salt and pepper.
Remove the cooked chicken from the skillet and set aside.
If needed, add the remaining 1 tablespoon olive oil to the skillet, then add the zucchini and bell peppers.
Sauté the vegetables until tender and lightly browned, about 5 minutes.
Add 1 tablespoon pesto to the vegetables and toss to coat evenly.
Move the vegetables to the side of the skillet, return the chicken to the pan, and add the remaining 1 tablespoon pesto to the chicken; stir to combine and heat through.
Adjust seasoning with salt and pepper if needed, then remove from heat and garnish with chopped parsley before serving.