Trapped ions can be cooled close to their motional ground state, which is imperative in implementing quantum computation and quantum simulation. Here, we theoretically investigate the capability of light-mediated chiral couplings between ions to enable a superior cooling scheme exceeding the single-ion limit of sideband cooling. Under asymmetric driving, the target ion manifests the chiral-coupling-assisted refrigeration at the price of heating others, where its steady-state phonon occupation outperforms the lower bound set by a single ion. We further explore the optimal operation conditions for the refrigeration where a faster rate of cooling can still be sustained. Under an additional nonguided decay channel, a broader parameter regime emerges to support the superior cooling and carries over into the reciprocal coupling, suppressing the heating effect instead. Our results present a tunable resource of collective chiral couplings which can help surpass the bottleneck of the cooling procedure and open up new possibilities in applications of trapped-ion-based quantum computation and simulation.