Season the chicken breasts with salt and pepper.
Cook the chicken: pan-fry over medium heat, grill, or bake at 200°C (400°F) until cooked through (about 12–20 minutes depending on method); then transfer to a plate and let cool slightly.
Once cool enough to handle, cut the chicken into bite-sized cubes.
Trim and roughly chop the celery, then pulse in a blender or food processor until finely chopped (or finely chop by hand).
In a mixing bowl, combine the chopped celery, mayonnaise, curry powder, and finely chopped basil; season with salt and pepper to taste and mix until smooth.
Toss the cubed chicken in the curry-celery sauce until evenly coated.
Serve the dressed chicken over a bed of salad mix.