Mix the turmeric and remaining ingredients with the cane sugar. Set aside 1 tbsp in a bowl. Mix the oil and rum into the remaining spice mixture. Add the meat, mix, cover and leave to marinate in the fridge for about 1 hr.
Heat the oil in a non-stick frying pan. Fry the chicken in batches over a medium heat for about 5 mins. on each side, remove, salt. Add a little oil if necessary. Add the celery, stir fry for approx. 3 mins., then remove.
Combine the lime juice, oil and ginger with the reserved spice mixture. Add the chicken, celery and melon, mix, season.