Bring a large pot of salted water to a boil and cook the whole wheat penne according to package directions until al dente.
While pasta cooks, heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then sauté until cooked through (about 5-7 minutes). Remove chicken from skillet and set aside.
In the same skillet, reduce heat to medium. Add shallots and garlic, sautéing for 2 minutes until fragrant.
Stir in the tomato paste and red pepper flakes, cooking for 2-3 minutes until the paste darkens slightly.
Pour in the vodka to deglaze the pan, scraping up any browned bits. Simmer for 2 minutes until the liquid is reduced by half.
Whisk in the chicken broth and then the Greek yogurt until a smooth sauce forms. Lower heat to prevent the yogurt from curdling.
Add the cooked pasta and chicken to the skillet, tossing well to coat with the sauce.
Stir in the fresh basil and Parmesan cheese. Serve immediately.