We have investigated the valence, spin, and orbital state of the Co ions in the one-dimensional cobaltate Ca3Co2O6 using x-ray absorption and x-ray magnetic circular dichroism at the Co-L2,3 edges. The Co ions at both the octahedral Co_oct and trigonal Co_trig sites are found to be in a 3+ state. From the analysis of the dichroism we established a low-spin state for the Co_oct and a high-spin state with an anomalously large orbital moment of 1.7 muB at the Co3+ trig ions. This large orbital moment along the c-axis chain and the unusually large magnetocrystalline anisotropy can be traced back to the double occupancy of the d2 orbital in trigonal crystal field.