For a graph (Formula presented.), a Roman dominating function (Formula presented.) has the property that every vertex (Formula presented.) with (Formula presented.) has a neighbor (Formula presented.) with (Formula presented.). The weight of a Roman dominating function (Formula presented.) is the sum (Formula presented.), and the minimum weight of a Roman dominating function on (Formula presented.) is the Roman domination number of (Formula presented.). In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower Roman irredundance numbers, and then develop a Roman domination chain parallel to the well-known domination chain. We also develop sharpness, strictness and bounds for the Roman domination chain inequalities.