Bring a medium pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente.
While the pasta cooks, place a large skillet over medium heat and add the diced pancetta, cooking until the fat renders and the meat is golden brown.
Add the diced chicken breast to the skillet with the pancetta and sear until cooked through and lightly browned on all sides.
Push the meat to the edges of the pan and add the olive oil, minced onion, and minced garlic to the center, sautéing for 2 minutes until fragrant.
Pour in the vodka to deglaze the pan, scraping up any browned bits from the bottom, and allow the liquid to reduce by half.
Stir in the tomato puree, red pepper flakes, sea salt, and black pepper, then let the sauce simmer on low for 5 minutes.
Remove the skillet from the heat and stir in the Greek yogurt until the sauce is smooth and creamy.
Toss the cooked pasta into the sauce until well coated and serve immediately topped with freshly chopped basil.