Among noncentrosymmetric structures, chirality has recently been recognized as a novel source of asymmetrical charge/spin transports as exemplified by electrical magnetochiral anisotropy (EMChA) and chirality-induced spin selectivity. Although similar bulk-charge rectification and the Rashba-Edelstein effect in polar systems are quantitively reproducible by theory based on the electronic band structures, the relevance of band parameters in chiral effects remains elusive. Here, by working with a chiral organic superconductor, we experimentally demonstrate a gigantic EMChA and large superconducting diode effect, both of which are difficult to be explained solely by its band parameters. A two-critical-current signature and an enhanced critical field suggested triplet-mixed Cooper pairs with anomalously enhanced spin-orbit coupling above atomic limit. Our results clearly highlight a unique spin-momentum locking with large stiffness beyond the expectation, suggesting an unknown driving force for spin polarization inherent to chirality.