Periodic Hartree-Fock and DFT based calculations reveal that KO3 is a strongly ionic insulator with a gap of approximately 3.0 eV. Despite its relatively simple crystal structure, the presence of molecular paramagnetic O-3(-) anions gives rise to a complex magnetic net of'S = 1/2 spins for KO3. Analysis of the different exchange coupling interactions points toward a significant 1D character for the magnetic behavior of this compound.