Prepare the relish at least one day in advance. The relish will keep, covered and refrigerated, for one week.
Using a small food processor, roughly chop the cranberries. Add the sugar, horseradish and lemon juice. Pulse to combine. Transfer the relish to a storage container and refrigerate at least one day. Serve at room temperature.
Chicken and Marinade
Combine the marinade ingredients in a small bowl.
Trim any fat from the chicken and gently pound to an even thickness. Place the chicken in a resealable plastic bag and add the marinade. Marinate for at least one hour or up to four hours.
Remove the chicken from the marinade and pat dry; season with salt and pepper.
Preheat the grill for medium high (375 degrees F.) direct cooking.
Grill the chicken for seven to eight minutes per side or to an internal temperature of 165 degrees F. Transfer the chicken to a warmed platter and bring to the kitchen. Tent the chicken with foil and let it rest for five minutes before serving.