Magnetochiral dichroism (MChD) is a nonreciprocal manifestation of light-matter interaction that can be observed in chiral magnetized systems. It features a differential absorption of unpolarized light depending on the relative orientation of the magnetic field and the light wavevector and on the absolute configuration of the system. The relevance of this effect for optical readout of magnetic data calls for a complete understanding of the microscopic parameters driving MChD with an easy-accessible and nondamaging light source, such as visible light. For this purpose, here we report on MChD detected with visible light on a chiral magnetic helix formulated as [MnIII(cyclam)(SO4)]ClO4·H2O (cyclam = 1,4,8,11-tetraazacyclotetradecane) featuring antiferromagnetically coupled anisotropic MnIII ions. Alternate current susceptibility measurements revealed the existence of a single-chain magnet behavior hidden below the canted antiferromagnetism (TN = 5.8 K) already evidenced by direct current magnetometry. A detailed analysis of the optical absorption gives access to the value of the zero-field splitting parameter D (2.9 cm-1), which quantifies the magnetic anisotropy of the MnIII centers. Below the magnetic ordering temperature of the material, the MChD spectra exhibit intense absolute configuration dependent MChD signals reaching record values of ca. 12% of the absorbed intensity for the two electronic transitions most influenced by the spin-orbit coupling of the MnIII ion. These findings set a clear route toward the design and preparation of highly MChD-responsive molecular materials.