Step 1

To prepare salsa: Working over a medium nonreactive bowl, supreme grapefruit (see Tips). Squeeze the membranes to extract any extra juice. Drain all the juice into a separate bowl and set aside. Add tomato, bell pepper, jalapeño, onion, lime juice and 1/2 teaspoon salt to the fruit; mix well. Refrigerate for at least 30 minutes and up to 2 hours. Stir in cilantro just before serving.

Step 2

To prepare fajitas: Cut chicken in half horizontally, holding the knife parallel to the cutting board. Place the chicken between 2 large pieces of plastic wrap. Pound with the smooth side of a meat mallet or a heavy saucepan to an even 1/4-inch thickness.

Step 3

Combine oil, garlic, oregano and the reserved grapefruit juice in a large shallow nonreactive dish. Add the chicken to the marinade; turn to coat well. Cover and refrigerate for at least 1 hour and up to 2 hours.

Step 4

Preheat grill to medium-high or heat a grill pan over medium-high heat. Remove the chicken from the marinade and let stand at room temperature while the grill heats. (Discard marinade.)

Step 5

Season the chicken with salt and pepper. Oil the grill rack (or pan). Grill the chicken, turning once, until just cooked through, 5 to 7 minutes total.

Step 6

Transfer the chicken to a clean cutting board. Slice crosswise into 1/2-inch-thick strips. Serve with tortillas and the grapefruit salsa, garnished with radishes and/or jicama, if desired.