Heat the oil in a wok or large pot at medium-high heat and add the garlic, ginger and curry paste, and stir until fragrant.
Add the coconut milk, broth, and makrut lime leaves. Stir until the curry paste is mixed into the liquid and it comes to a simmer.
Reduce the heat to medium and add the chicken pieces, potatoes and leeks, cover and cook for 5 minutes.
Add the fish sauce, sugar, and peppers, stirring in well, cover and cook for 5-10 minutes, or until chicken is fully cooked.
Take off the heat, squeeze in the lime juice and serve with rice.