If you are cooking it in the oven, you are baking it. You can only grill it on some sort of grill, usually over an open flame.
In the US we call grilling in a closed oven "broiling," but in the UK it's often called grilling. But it's the same method of cooking.
The term "grill" can vary in meaning, but generally it refers to cooking something over dry heat at a higher heat, without using a liquid like water, milk or oil to transfer heat to the item being cooked (those methods are known in English as boiling, poaching and frying, respectively ). In the US, and in many countries, we do most of our grilling on outdoor grills of some sort, but technically what we think of as "broiling" in an oven (that is equipped for broiling--something not quite as common in the US as when I was younger) is a form a grilling too, as it uses the same method of heat transfer.
(Comparatively, baking or roasting are cooking methods that use much lower heat and longer cooking times than grilling/broiling, and rely more of heat convection (heat transfer via air or liquid surrounding the food) than conduction, which grilling/broiling does, hence requiring a higher heat.)
I suppose the oven broiler, especially in a gas oven, is really just a sort of inverted grill, though the grill supporting the food is on the opposite side from the heat source. I must admit that I always think of the metal grill when I think of grilling, well that and the martyrdom of St Lawrence, patron of cooks and comedians, who told his persecutors to flip him when one side was done. I'm sure he only said so once, in order not to dry out.
Thats what I was thinking. But maybe its not needed cause of the context. Maybe the oven is only used for chicken or maybe they only cook chicken in the oven (Not stovetop)