The compound La3Re2O10 has been synthesized by solid-state reaction and characterized by powder neutron diffraction, SQUID magnetometry, and heat capacity measurements. Its structure consists of isolated [Re2O10](9-) dimer units of two edge-shared ReO6 octahedra, separated by La3+ within the lattice. The Re-Re distance within the dimer units is 2.488 angstrom, which is indicative of metal-metal bonding with a bond order of 1.5. The average oxidation state of the Re atom is +5.5, leaving one unpaired electron per dimer unit (S = 1/2). Although the closest interdimer distance is 5.561 angstrom, the magnetic susceptibility data and heat capacity measurements indicate this compound exhibits both short- and long-range magnetic order at surprisingly high temperatures. The zero field cooled (ZFC) magnetic susceptibility data show two broad features at 55 and 105 K, indicating short-range order, and a sharper cusp at 18 K, which signifies long-range antiferromagnetic order. The heat capacity of La3Re2O10 shows a A-type anomaly at 18 K, which is characteristic of long-range magnetic order. DFT calculations determined that the unpaired electron resides in a pi-bonding orbital and that the unpaired electron density is widely delocalized over the atoms within the dimer, with high values at the bridging oxygens. Extended Huckel spin dimer calculations suggest possible interaction pathways between these dimer units within the crystal lattice. Results from the calculations and fits to the susceptibility data indicate that the short-range magnetic ordering may consist of 1-D antiferromagnetic linear chains of coupled S = 1/2 dimers. The magnetic structure of the antiferromagnetic ground state could not be determined by unpolarized neutron powder diffraction.