Local chromatin compaction undergoes dynamic perturbations to regulate genetic processes. To address this, the direct measurement of the fluidity of chromatin structure is carried out in single live cells using steady-state anisotropy imaging and polarization modulation microscopy. Fluorescently tagged core and linker histones are used to probe different structural aspects of chromatin compaction. A graded spatial heterogeneity in compaction is observed for the chromatin besides the distinct positional ordering of core and linker histones. These spatio-temporal features are maintained by active processes and perturbed during death. With cell cycle, the distribution in compaction heterogeneity continually changes maximizing during M-G1 transition where it displays bimodal behavior. Such measurements of spatio-temporal chromatin fluidity could have broader implications in understanding chromatin remodeling within living cells.