Rotation is an intrinsic property of stars and provides essential constraints on their structure, formation, evolution and interaction with the interplanetary environment. The Sun provides a unique opportunity to explore stellar rotation from the interior to its atmosphere in great detail. We know that the Sun rotates faster at the equator than at the poles, but how this differential rotation behaves at different atmospheric layers within it is not yet clear. Here we extract the rotation curves of different layers of the solar photosphere and chromosphere by using whole-disk Dopplergrams obtained by the Chinese Hα Solar Explorer (CHASE) for the wavebands Si i (6,560.58 Å), Hα (6,562.81 Å) and Fe i (6,569.21 Å) with a spectral resolution of 0.024 Å. We find that the Sun rotates progressively faster from the photosphere to the chromosphere. For example, at the equator, it increases from 2.81 ± 0.02 μrad s⁻¹ at the bottom of the photosphere to 3.08 ± 0.05 μrad s⁻¹ in the chromosphere. The ubiquitous small-scale magnetic fields and the height-dependent degree of their frozen-in effect with the solar atmosphere are plausible causes of the height-dependent rotation rate. The results have important implications for understanding solar subsurface processes and solar atmospheric dynamics.