In pressure cooker on saute setting over high heat, bring broth and rice bags to boil. Boil, uncovered, 10 minutes. Remove bags with fork and set aside.
Add coconut milk, curry paste, soy sauce and brown sugar to pressure cooker. Turn off saute setting. Add chicken. Cover and lock to seal. Set to pressure cook setting over high heat about 10 minutes, or until chicken is tender. Carefully, manually or naturally, release pressure according to manufacturer's instructions before removing lid.
Set pressure cooker to saute setting over medium heat. Remove chicken and shred with two forks; add to soup along with lime juice and green onions. Remove rice from bags and stir into soup. Simmer until rice is heated through.