Whisk together the soy sauce, cilantro, garlic, brown sugar, vegetable oil and lime juice in a bowl.
In a large baking dish, arrange the ribeye pork chops in an even layer. Pour the marinade over the pork chops, reserving about 1/4 cup of the marinade in the refrigerator for later use.
Marinate the pork chops for 20 to 30 minutes.
Heat an indoor grill pan or outdoor grill to medium-high heat. Remove pork chops from the marinade, discarding the excess marinade. Place pork chops on the hot grill for 4 minutes on each side, flipping once until the internal temperature of the pork measures between 145 degrees F. (medium rare) and 160 degrees F. (medium) on a meat thermometer.
Transfer the grilled pork chops to a cutting board and let rest for 3 minutes before slicing against the grain.
Pour the reserved marinade over the sliced pork before serving.