Cut the jicama into chunks, and then pulse in the food processor until finely ground. Transfer to a large bowl.
In the same processor carafe, pulse the parsley and mint until finely chopped. Add to the jicama along with the tomatoes, cucumbers, onions, 2 tablespoons of the oil, the lemon juice, 2 teaspoons salt and 3/4 teaspoon pepper.
Stir together the remaining 2 tablespoons oil with the paprika, 1 teaspoon salt and 1/2 teaspoon pepper and rub all over chicken.
Preheat a grill to medium-high heat.
Grill the chicken, turning, until grill marks appear, about 4 minutes. Let the chicken rest 5 minutes.