Bring a pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente.
While the pasta cooks, dice the chicken breast into bite-sized pieces and mince the garlic cloves.
Heat the olive oil in a large skillet over medium-high heat, then add the chicken and garlic, sautéing until the chicken is golden and cooked through.
In a blender, combine the roasted red peppers, Greek yogurt, nutritional yeast, sea salt, and black pepper, blending until the sauce is completely smooth.
Drain the pasta, reserving a small splash of the cooking water, and add the pasta to the skillet with the chicken.
Pour the red pepper sauce over the chicken and pasta, tossing well to coat and adding a splash of pasta water if needed to reach a velvety consistency.
Serve the pasta immediately topped with freshly chopped basil.