The design of antiferromagnetic nanomaterials preserving large orbital magnetic moments is important to protect their functionalities against magnetic perturbations. Here, we exploit an archetype H6HOTP species for conductive metal-organic frameworks to design a Co-HOTP one-atom-thick metal-organic architecture on a Au(111) surface. Our multidisciplinary scanning probe microscopy, X-ray absorption spectroscopy, X-ray linear dichroism, and X-ray magnetic circular dichroism study, combined with density functional theory simulations, reveals the formation of a unique network design based on threefold Co+2 coordination with deprotonated ligands, which displays a large orbital magnetic moment with an orbital to effective spin moment ratio of 0.8, an in-plane easy axis of magnetization, and large magnetic anisotropy. Our simulations suggest an antiferromagnetic ground state, which is compatible with the experimental findings. Such a Co-HOTP metal-organic network exemplifies how on-surface chemistry can enable the design of field-robust antiferromagnetic materials.