Peel and core the melon, if necessary cut out a few small balls for the garnish, coarsely dice the remaining pulp. Puree the melon pulp with lime juice, lime zest and chilli in a blender until smooth, season with salt and pepper. Cover the puree and put it in a cool place for about an hour.
Puree the basil leaves with the yoghurt, season with salt and pepper.
Just before serving, add the sparkling wine to the melon puree, serve the cold bowl with a dollop of basil yoghurt and the melon balls.