Time-resolved profiles of the Balmer series Hα line emitted by a laser-produced hydrogen plasma have been measured to determine the shift and width for electron densities from below 1018 to above 1020 cm−3 at an average temperature of 28000 K. Fits of the profiles that allow for self-absorption in the plasma yield shifts and widths that are consistent with experiments on lower density and cooler gas-liner pinch plasmas. The width scales as and the shift as between and cm−3. Hα shifts monotonically and nearly linearly to the red with increasing density under the reported conditions. A comparison to theory calculations using exact potentials for shows that an intrinsic asymmetry becomes significant only in the upper limit of this range when a satellite develops in the far red wing.