Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Season the chicken with salt and pepper and add to the pot. Cook, stirring occasionally, until browned, about 8 minutes. Add the curry powder and half of the garlic. Cook, stirring, until the garlic softens slightly, about 1 minute.
Stir the chickpeas and their liquid into the pot and bring to a boil. Reduce the heat to medium low; cover and cook until the chicken is tender, about 12 minutes.
Meanwhile, puree the remaining garlic, the cilantro, 2 tablespoons olive oil, the lime juice and vinegar in a mini food processor or blender until a paste forms. Heat the remaining 2 tablespoons olive oil in a small skillet over medium heat. Add the cilantro paste; cook until dark green, about 1 minute. Transfer to a medium bowl and add the coleslaw mix; season with salt and toss to coat.
Top each serving of the chicken curry with the slaw mixture, some hot pepper sauce and cilantro. Serve with the naan.