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Slice the duck breast into thin strips.
Heat the vegetable oil in a large pan or wok over medium heat.
Add the red curry paste and cook for 1-2 minutes, until fragrant.
Add the sliced duck breast and cook for 3-4 minutes, until browned.
Pour in the coconut milk and bring to a simmer.
Add the fish sauce, palm sugar, and kaffir lime leaves.
Simmer for 10-15 minutes, until the duck is cooked through and tender.
Garnish with Thai basil leaves and sliced red chilies.
Serve hot with jasmine rice.