Preheat grill to medium-high heat, approximately 375° to 400° Fahrenheit.
Add ¼ teaspoon cayenne pepper, ¼ teaspoon paprika, ¼ teaspoon garlic powder, ¼ teaspoon onion powder, ½ teaspoon salt, and ¼ teaspoon freshly ground black pepper to small mixing bowl. Whisk ingredients together until well blended.
Remove chicken from pickle juice marinade and pat chicken breasts completely dry on all sides with paper towels. Place chicken breasts on large plate.
Season chicken breasts generously on all sides with prepared spice blend. Rub or pat spice blend into chicken to ensure coverage.
Lightly spray grill rack with neutral-flavored spray oil, then place seasoned chicken breasts on grill rack over indirect heat. Grill chicken breasts 5 minutes.
Flip chicken breasts over and grill 5 to 8 minutes more, or until internal temperature reaches 158° to 160° Fahrenheit.
Once chicken reaches 158° to 160° Fahrenheit internally, carefully remove chicken from grill and place on cutting board. Set chicken aside to rest 5 minutes.
After 5 minutes, slice chicken breasts into strips or bite-sized chunks.