In a medium bowl, combine the yogurt, lime zest, chilli flakes, salt and pepper. Stir to combine. Add the chicken and toss to coat. Cover the bowl and refrigerate for 30 minutes or overnight if preferred.
Place the marinated chicken fillets on the grill. Cover with the lid and grill for about 5 minutes. Flip the chicken over. Cover and grill until the chicken is cooked through and feels firm to touch, about 4 minutes. Transfer the chicken to a cutting board. Let rest for 5 minutes.
Place the chicken on a serving platter, and then spoon some chutney alongside the chicken.