The solar chromosphere was daily observed in the Ca ii K line at the Mount Wilson Observatory from 1915 August to 1985 July. A digitized data base was created, which includes synoptical maps of the chromosphere in Ca ii intensity from Carrington rotations 827 to 1764. We have used the data base to investigate rotation and its differential of the chromosphere and the quiet chromosphere. The chromosphere is found to rotate faster than sunspots, but the difference in their rotation rates decreases with decreasing latitude, and near the equator they rotate at nearly the same speed. The chromosphere is obviously faster than the quiet photosphere and slightly faster than the quiet chromosphere at low latitudes, but slightly slower than the quiet chromosphere at middle latitudes. The differential degree of the rotation rate at low latitudes, ranging from largest to smallest in order, is found to be: sunspots, the chromosphere, the quiet photosphere, and the quiet chromosphere. The differential of the rotation rate is found to be different in different solar cycles for the chromosphere and the quiet chromosphere. Helioseismology observations suggest that these findings are plausible.