A global ¼°ocean/sea-ice 50-member ensemble simulation is analyzed to disentangle the imprints of the atmospheric forcing and the chaotic ocean variability on regional sea level trends over the satellite altimetry period. We find that the chaotic ocean variability may mask atmospherically forced regional sea level trends over 38% of the global ocean area from 1993 to 2015, and over 47% of this area from 2005 to 2015. These regions are located in the western boundary currents, in the Southern Ocean and in the subtropical gyres. While these results do not question the anthropogenic origin of global mean sea level rise, they give new insights into the intrinsically oceanic versus atmospheric forcing of regional sea level trends and provide new constraints on the measurement time required to attribute regional sea level trends to the atmospheric forcing or to climate change. Plain Language Summary As a direct consequence of anthropogenic influences, global mean sea level rises in response to ocean warming and land ice melting. Since the early 1990s, satellite altimetry has revealed large regional contrasts in sea level trends, controlled by temperature and salinity changes, oceanic processes and atmospheric forcing. Using an ensemble of forced eddying ocean simulations, we show that regional sea level trends over the altimetric period are only partly determined by the atmospheric evolution (both natural and anthropogenic): nonlinear ocean processes produce additional sea level trends that are inherently random, which can compete in certain regions with the externally forced trends. These results do not question the existence of global and regional sea level trends, but suggest that sea level trends may not be unambiguously attributed to external causes in certain regions.