The highest-density magnetic storage media will code data in single-atom bits. To date, the smallest individually addressable bistable magnetic bits on surfaces consist of 5-12 atoms. Long magnetic relaxation times were demonstrated in molecular magnets containing one lanthanide atom, and recently in ensembles of single holmium (Ho) atoms supported on magnesium oxide (MgO). Those experiments indicated the possibility for data storage at the fundamental limit, but it remained unclear how to access the individual magnetic centers. Here we demonstrate the reading and writing of individual Ho atoms on MgO, and show that they independently retain their magnetic information over many hours. We read the Ho states by tunnel magnetoresistance and write with current pulses using a scanning tunneling microscope. The magnetic origin of the long-lived states is confirmed by single-atom electron paramagnetic resonance (EPR) on a nearby Fe sensor atom, which shows that Ho has a large out-of-plane moment of (10.1±0.1) μB on this surface. In order to demonstrate independent reading and writing, we built an atomic scale structure with two Ho bits to which we write the four possible states and which we read out remotely by EPR. ... mehrThe high magnetic stability combined with electrical reading and writing shows that single-atom magnetic memory is possible.