Heat grill to medium. In medium bowl, whisk together oil, paprika, cumin, brown sugar, oregano, onion powder, cayenne pepper, and ½ teaspoon each salt and black pepper. Add 1 chicken breast at a time and coat with spice rub.
Grill chicken, covered, until cooked through (165°F on instant-read thermometer), 8 to 9 minutes per side. Transfer to cutting board and let rest 10 minutes before cutting into bite-size pieces.
In small bowl, combine sour cream, lime zest, and 1 tablespoon juice, adding additional juice if desired.
Serve chicken with lime crema and lettuce leaves and cilantro if desired.
