Polymorphism refers to the occurrence of multiple chemically identical but structurally distinct phases. Diamond and graphite are well-known examples. Recently, configuration disorder was compositionally engineered into single lattices, leading to the discovery of high-entropy alloys (HEAs). For these novel entropy-stabilized forms of crystalline matter with extremely high structural stability, is polymorphism still possible? Here, by employing an in situ high-pressure synchrotron radiation X-ray diffraction (XRD) technique in a diamond anvil cell, we discover a polymorphic transition from fcc-to-hcp structures in the prototype CoCrFeMnNi HEA.The transition is irreversible, and our in situ high-temperature synchrotron radiation XRD experiments at different pressures of the retained hcp HEA unambiguously reveal that the fcc phase is a stable polymorph at high temperatures, while the hcp structure is thermodynamically more favorable at lower temperatures. As the pressure is increased, the critical temperature for the hcp-to-fcc transformation also rises.