In a large saucepan, bring 2 3/4 cups water to a boil. Salt the water, then stir in the squash and bulgur. Cover and simmer until squash and bulgur are tender, 10 to 12 minutes. Drain and stir in the chickpeas. Spread out the bulgur mixture on a large plate and let cool slightly.
Meanwhile, season the chicken with salt and pepper. In a medium skillet, heat the EVOO over medium. Add the chicken, skin side down, and cook, turning once or twice, until the skin is crispy and the chicken is cooked through, about 20 minutes. Let the chicken stand 5 minutes. Cut the chicken off the bone, then cut into bite-size cubes.
Transfer the bulgur mixture to a large bowl. Stir in the cubed chicken, parsley and lemon juice. Season with salt and pepper and toss well.