Make several crosswise cuts in the chicken thighs and place in a large bowl. Thinly grate the lime zest and reserve. Squeeze the limes and drizzle the juice over the meat. Sprinkle with the cayenne pepper. Cover and refrigerate for at least 2 hours or overnight. Peel the mangoes and cut them in half. Remove the stones and cut the flesh into strips.
Lift the thighs out of the marinade with a slotted spoon. Keep the marinade. Heat the oil in a large skillet and fry the thighs, turning several times, until golden brown all over. Add the marinade, lime zest, mango strips and sugar and stir in. Cover and simmer for 15 minutes, stirring occasionally.
Sprinkle with shredded coconut and parsley to taste and serve.