Bring a pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente, then drain and set aside.
In a large skillet over medium heat, add the diced pancetta and cook until crispy and the fat has rendered.
Add the cubed chicken breast to the skillet with the pancetta and sauté until the chicken is golden brown and cooked through.
Remove the chicken and pancetta from the pan and set aside, leaving the drippings in the pan.
Add the olive oil to the same skillet, then stir in the minced shallot and garlic, sautéing for 1-2 minutes until fragrant.
Pour in the vodka to deglaze the pan, scraping up any browned bits from the bottom, and let it simmer for 1 minute until reduced.
Stir in the tomato puree, sea salt, and black pepper, and let the sauce simmer on low for 5 minutes.
Remove the skillet from the heat and whisk in the Greek yogurt until the sauce is smooth and creamy.
Add the cooked pasta, chicken, and pancetta back into the skillet, tossing well to coat everything in the sauce.
Garnish with fresh basil chiffonade and serve immediately.