The idea of atoms defying ionization in ultrastrong laser fields has fascinated physicists for the last three decades. In contrast to extensive theoretical work on atoms stabilized in strong fields only few experiments limited to intermediate intensities have been performed. In this work we show exceptional stability of Rydberg atoms in strong laser fields extending the range of observation to much higher intensities. Corresponding field amplitudes of more than 1 GV/cm exceed the thresholds for static field ionization by more than 6 orders of magnitude. Most importantly, however, is our finding that a surviving atom is tagged with a measure of the laser intensity it has interacted with. Reading out this information removes uncertainty about whether the surviving atom has really seen the high intensity. The experimental results allow for an extension of the investigations on the stabilization and interaction of a quasifree electron with a strong field into the relativistic regime.