In a small food processor, food chopper, or blender pulse the tomatillos, cilantro, onion, lime juice, and jalapeno until tomatillos are processed to release juices. Add avocado and salt; pulse 8-10 times or to desired consistency.
Meanwhile, sprinkle the cumin and salt over both sides of the chicken breasts, rubbing the seasonings to coat.
Heat canola oil in a large skillet over medium heat. Once shimmering and hot, add the chicken and cook 3-5 minutes, or until browned. Flip and cook an additional 3-5 minutes or until chicken is cooked through. Serve hot with ¼ of the guacamole sauce over each chicken breast.