Heat the oil in a large saucepan over medium-high heat until shimmering. Add the bacon and cook, stirring occasionally, until rendered but not crisp, 3 to 5 minutes. Add the onion, carrot, celery, poblano, garlic and a generous pinch each of salt and pepper. Cook, stirring occasionally, until the vegetables soften and just start to brown, about 8 minutes. Stir in the cumin and coriander and cook, stirring, until fragrant, about 30 seconds.
Meanwhile, transfer the tomatoes and their juices to a medium bowl. Using your hands, gently crushed the tomatoes into chunks. Add the tomatoes, stock and chipotles to the pan and bring to a simmer.
Remove and discard the skin and bones from the chicken. Coarsely chop or shred the meat. Stir the chicken and chickpeas into the pan. Simmer over medium heat, stirring gently, until the chicken and chickpeas are heated through, 3 to 5 minutes. Season the chili with salt and pepper. Serve hot, topped with the cheese.