Bring a pot of salted water to a boil and cook the chickpea spaghetti according to package directions, reserving 1/4 cup of pasta water before draining.
While pasta cooks, heat olive oil in a large skillet over medium heat and add the diced pancetta, cooking until it becomes golden and crispy.
Add the diced chicken breast to the skillet with the pancetta, seasoning with half of the salt and pepper, and sauté until cooked through.
Stir in the minced garlic and cook for 1 minute until fragrant, then add the baby spinach and toss until just wilted.
In a small bowl, whisk together the Greek yogurt, Parmesan cheese, and the reserved pasta water until smooth.
Reduce the skillet heat to low, add the drained pasta, and pour the yogurt mixture over the top, tossing everything together until the sauce is creamy and well-combined.
Season with the remaining salt and pepper before serving warm.