Place pineapple wedges on a utility platter and squeeze lime juice over them. Mix together salt, ground black pepper, cumin, oregano, garlic powder, and onion powder to make fajita seasoning. Sprinkle fajita seasoning on the pineapple.
Grill the chicken until cooked through and the pineapple until the outside begins to caramelize.
While the chicken and pineapple are grilling, put the butter and oil in a large skillet and turn the heat to medium-high. Add the shallots and mushrooms and cook stirring occasionally, until they are soft, about 3 minutes. Add the green peppercorns and cook for 30 seconds. Add the mustard, cream and demi-glace and cook, stirring for 30 seconds.
Spoon sauce over chicken, with pineapple as an accompaniment. Garnish with chopped chives.