In a large skillet, heat oil over medium-high heat. Brown chicken in batches. Transfer to a 4- or 5-qt. slow cooker. Add poblanos and onion to drippings; cook and stir until crisp-tender, 4-5 minutes. Add garlic; cook 1 minute longer.
Remove from heat; add brandy. Cook over medium-high heat, stirring to loosen browned bits from pan. Stir in chili garlic sauce and chili paste; pour over chicken.
Cook, covered, on low until a meat thermometer inserted into chicken reads 165°, 4-5 hours.