A fixture support assembly for supporting a lighting or fan fixture on a drop ceiling having a grid supporting structure. The assembly includes a U-shaped bar with an upward directed channel and a channel bottom, two end brackets integral with the bar, a clamp member slidable within the channel, and an electrical box. The end brackets include an inner leg for resting on the horizontal ledges of adjacent T-rails and outer legs for loosely fitting over the top of the T-rails. A slot is provided in the channel bottom extending from one end to slightly past the center of the bar. A fastening arrangement connects the electrical box to the clamp member and in a loosened state enables positioning of the electrical box with respect to the bar.