We present photometric and spectroscopic observations of the members of three previously cataloged compact group (CG) candidates at redshifts z > 0.3. These confirm spectroscopic redshifts compatible with being gravitationally bound structures at redshifts 0.3112, 0.3848, and 0.3643, respectively, and then they are the most distant CGs known with spectroscopic confirmation for all their members. The morphological and spectroscopic properties of all their galaxies indicate early types dominated by an old population of stars, with little star formation or nuclear activity. Most of the physical properties derived for the three groups are quite similar to the average properties of CGs at lower redshifts. In particular, from the velocities and positions of the respective members of each CG, we estimate short dynamic times. These leave open the questions of identifying the mechanism for forming CGs continuously and the nature of the final stages of these structures.