Bring a large pot of salted water to a boil. Add the whole wheat penne pasta and cook according to package instructions until al dente, about 9-11 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Add the chicken breast pieces to the skillet, season with salt and freshly ground black pepper, and cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned.
Add the minced garlic to the skillet with the chicken and cook for 1 minute until fragrant.
Add the diced zucchini and halved cherry tomatoes to the skillet. Cook for 4-5 minutes until the vegetables are tender but still crisp.
Reduce the heat to medium and stir in the baby spinach leaves. Cook until wilted, about 1-2 minutes.
Add the cooked pasta to the skillet and toss to combine with the chicken and vegetables.
Stir in the lemon zest, lemon juice, crushed red pepper flakes, dried oregano, and chopped fresh parsley. Adjust seasoning with additional salt and pepper if needed.
Remove from heat and serve immediately.