Slice the cucumber in half lengthways and use a teaspoon to scoop out the seeds. Slice cucumber into thick diagonal chunks. Tip it into a bowl and sprinkle with the sugar, vinegar and large pinch of salt. Leave for about 30 mins in the fridge. Meanwhile, tip the other salad ingredients into a bowl. Drain the cucumber and tip in with the rest of the ingredients.
Heat a griddle pan or heavy-bottomed frying pan until hot, but not smoking. Rub the chicken with oil, season with salt and pepper and sear, skin-side down, for about 8 mins until the skin is crisp and brown and the chicken is practically cooked. Flip the chicken over and give it a few mins more on the flesh side to finish it off. Leave the chicken to rest, then slice each breast on an angle and serve with a pile of cucumber salad.