The 5d magnetic oxide Ca3LiOsO6 has a trigonal arrangement of its LiOsO6 chains parallel to the c-direction and hence has triangular arrangements of high-spin Os5+ (d(3)) ions but exhibits no spin frustration and undergoes a long-range antiferromagnetic ordering at a high temperature. The origin of this apparently puzzling observation was examined by evaluating the nearest-neighbor Os-O center dot center dot center dot O-Os spin exchange interactions of Ca3LiOsO6 on the basis of density functional calculations. Our study shows that, of the two nearest-neighbor interchain spin exchanges, one dominates over the other and that the intrachain spin exchange and the dominating interchain spin exchange are strong and form a three-dimensional antiferromagnetic spin lattice with no spin frustration, which is responsible for the long-range antiferromagnetic ordering of Ca3LiOsO6 at high temperature. In determining the strengths of the Os-O center dot center dot center dot O-Os exchange interactions of Ca3LiOsO6, the Li+ and Ca2+ ions of the O center dot center dot center dot Li+center dot center dot center dot O and O center dot center dot center dot Ca2+center dot center dot center dot O linkages are found to play only a minor role.