We have studied the electronic structure and magnetism of the spin chain compounds Ca3ZnMnO6 and Ca3ZnCoO6 using density functional theory with generalised gradient approximation (GGA). In agreement with experiment our calculations reveal that high spin (HS) state for Mn(4+) ion and low spin (LS) state for Co(4+) ion stabilize the magnetic structure of the respective compounds. The magnetic exchange paths, calculated using Nth order muffin-tin orbital downfolding method, shows dominant intra-chain exchange interaction between the magnetic ions (Mn, Co) is antiferromagnetic for Ca3ZnMnO6 and ferromagnetic for Ca3ZnCoO6. The magnetic order of both the compounds is in accordance with the Goodenough-Kanamori-Anderson rules and is consistent with the experimental results. Finally we have investigated the importance of spin-orbit coupling (SOC) in these compounds. While SOC practically has no effect for the Mn system, it is strong enough to favor the spin quantization along the chain direction for the Co system in the LS state.