Heat vegetable oil in a large saucepan over medium heat. Stir in curry paste and minced ginger; cook and stir for 2 minutes. Stir in the cubed chicken, and cook until the pieces turn white on the outside, about 3 minutes.
Stir in brown sugar, fish sauce, tamarind paste, peanut butter, potatoes, and coconut milk. Bring to a boil, then reduce heat to medium-low, cover, and simmer until the potatoes are tender and the chicken pieces are no longer pink in the center, about 20 minutes.
Add the lime juice and cook for an additional 5 minutes before serving