Inverse Compton cooling limits the brightness temperature of the radiating plasma to a maximum of 10^11.5 K. Relativistic boosting can increase its observed value, but apparent brightness temperatures much in excess of 10¹³ K are inaccessible using ground-based very long baseline interferometry (VLBI) at any wavelength. We present observations of the quasar 3C 273, made with the space VLBI mission RadioAstron on baselines up to 171,000 km, which directly reveal the presence of angular structure as small as 26 μas (2.7 light months) and brightness temperature in excess of 10¹³ K. These measurements challenge our understanding of the non-thermal continuum emission in the vicinity of supermassive black holes and require a much higher Doppler factor than what is determined from jet apparent kinematics.