Geologic carbon storage is required for achieving negative CO2 emissions to deal with the climate crisis. The classical concept of CO2 storage consists in injecting CO2 in geological formations at depths greater than 800 m, where CO2 becomes a dense fluid, minimizing storage volume. Yet, CO2 has a density lower than the resident brine and tends to float, hindering the widespread deployment of geologic carbon storage. Here, we propose for the first time to store CO2 in supercritical reservoirs to eliminate the CO2 leakage risk. Supercritical reservoirs are found at drilling-reachable depth in volcanic areas, where high pressure (p>21.8 MPa) and temperature (T>374 ºC) imply CO2 is denser than water. We estimate that 100 injection wells could eventually provide a CO2 storage capacity in the range of 50-500 Mt yr-1. Carbon storage in supercritical reservoirs is an appealing alternative to the traditional approach.