Zest the lime into a bowl and squeeze in the juice. Keep the used lime halves for later. Peel and grate the ginger. Halve the chilli and flick out the seeds. Finely chop the chilli and add to the bowl along with the red curry paste. Pour in 1 tsp oil and 1 tbsp water. Mix together. Set aside.
Trim and peel the carrots, then slice into batons. Tip into a bowl. Slice the cucumber into rough cubes and add to the carrots.
Peel and halve the papaya. Use a spoon to scoop out the seeds (see our tip below). Cut into thin strips and combine with the carrots and cucumber. Set aside.
Heat your grill to high. Put the chicken breasts on a chopping board. Cover with a large sheet of greaseproof paper. Bash the chicken breasts with a rolling pin (or something similarly heavy) till they're about 1½cm thick.
Slice the lime halves into small pieces and scatter on a baking tray. Rub the chicken with 1 tsp oil. Place them on top of the limes. Grill for 4-5 mins till golden brown, then turn and grill till the chicken is golden and cooked through.
Add the lime, chilli and ginger dressing to the papaya and veg. Toss together till everything is well coated.
Pile the salad onto plates. Shred the chicken with two forks and scatter it on top. Scatter with the mint leaves to garnish.