Preheat a grill or grill pan on medium heat.
Season chicken with oil, thyme, salt, and pepper.
In a sauté pan over low-medium heat, add the butter, brown sugar, and pineapple. Bring to a low simmer until the pineapple is soft and the sauce is golden brown. Then set aside.
Cook the chicken on both sides to an internal temperature of 160°F using a thermometer. Once done, place in the pan with the pineapple.
Return the pan to medium heat and toss to warm, coating the chicken with the sauce.
Serve with rolls. Garnish with parsley.