Place a large saucepan or wok over medium heat. Add oil, garlic, shallot, and ginger and stir-fry about 1 minute. Add curry paste and stir-fry another 30 seconds, stirring constantly. Add coconut milk, chicken broth, sugar, fish sauce, and bell pepper and stir to combine. Add chicken. Bring to a boil, then lower to a simmer. Simmer uncovered about 30 minutes, until the chicken is cooked through and tender.