In this article we report for the first time experimental details concerning the synthesis and full characterization (including the single-crystal X-ray structure) of the spin-canted zigzag-chain compound [Co(H2L)(H2O)](infinity) [L = 4-Me-C6H4-CH2N(CPO3H2)(2)], which contains antiferromagnetically coupled, highly magnetically anisotropic Co(II) ions with unquenched orbital angular momenta, and we also propose a new model to explain the single-chain magnet behavior of this compound. The model takes into account (1) the tetragonal crystal field and the spin-orbit interaction acting on each Co(II) ion, (2) the antiferromagnetic Heisenberg exchange between neighboring Co(II) ions, and (3) the tilting of the tetragonal axes of the neighboring Co units in the zigzag structure. We show that the tilting of the anisotropy axes gives rise to spin canting and consequently to a nonvanishing magnetization for the compound. In the case of a strong tetragonal field that stabilizes the orbital doublet of Co(II), the effective pseudo-spin-1/2 Hamiltonian describing the interaction between the Co ions in their ground Kramers doublet states is shown to be of the Ising type. An analytical expression for the static magnetic susceptibility of the infinite spin-canted chain is obtained. The model provides an excellent fit to the experimental data on both the static and dynamic magnetic properties of the chain.