Experimental evidences are presented showing unusually large and highly anisotropic vibrations in the "simple cubic" (SC) unit cell adopted by calcium over a broad pressure ranging from 30-90 GPa and at temperature as low as 40 K. X-ray diffraction patterns show a preferential broadening of the (110) Bragg reflection indicating that the atomic displacements are not isotropic but restricted to the  plane. The unusual observation can be rationalized invoking a simple chemical perspective. As the result of pressure-induced s → d transition, Ca atoms situated in the octahedral environment of the simple cubic structure are subjected to Jahn-Teller distortions. First-principles molecular dynamics calculations confirm this suggestion and show that the distortion is of dynamical nature as the cubic unit cell undergoes large amplitude tetragonal fluctuations. The present results show that, even under extreme compression, the atomic configuration is highly fluxional as it constantly changes.