Heat oil in medium saucepan over medium high heat. Add curry paste, garlic, and ginger, and stir while cooking for 1-2 minutes until curry paste dries out and is fragrant.
Add chicken broth and coconut milk, stirring to dissolve the green curry paste into them.
Add the fish sauce, sugar, and lime leaves and stir to combine and allow to come to a simmer.
Add chicken, and reduce heat to medium or until bubbling gently. Cook for 8-10 minutes or until chicken flakes apart when you test it with a fork.
Add the snow peas and red bell pepper and cook for a further 3 minutes. Stir in lime or lemon juice. The curry won't be very thick, and that's the way it should be!
Serve with jasmine, basmati, or cauliflower rice.