Place the poblano peppers under a broiler, turning occasionally, until the skin is charred and blistered on all sides.
Place the charred peppers in a bowl and cover with a lid for 10 minutes to steam, then peel off the skin, remove the seeds, and roughly chop.
Bring a large pot of salted water to a boil and cook the chickpea spaghetti according to package directions until al dente.
While the pasta cooks, heat the olive oil in a large skillet over medium heat and sauté the diced chicken breast with sea salt and black pepper until cooked through.
Add the minced garlic and diced onion to the skillet with the chicken, cooking for 3 minutes until the onion is translucent.
In a high-speed blender, combine the roasted poblanos, Greek yogurt, and lime juice, blending until the sauce is completely smooth and vibrant green.
Drain the pasta, reserving a small amount of pasta water, and add the spaghetti and the poblano sauce to the skillet with the chicken.
Toss everything together over low heat until the sauce coats the noodles evenly, adding a splash of pasta water if needed to reach your desired consistency.
Divide the spaghetti into bowls and garnish with freshly chopped cilantro before serving.