Time-varying metamaterials have garnered significant attention for their ability to achieve anti-reflection in the time domain. However, current systems face limitations in spin-controlled manipulation, as most studies focus on non-chiral, time-varying metamaterials. Consequently, realizing spin-dependent broadband anti-reflection using time-varying chiral metamaterials remains underexplored. In this work, we propose a time-varying chiral structure composed of four temporal layers, each with distinct impedances and chiral parameters. By carefully adjusting these parameters across the layers, our structure enables broadband anti-reflection for both right- and left-circularly polarized (RCP and LCP) waves under small chiral conditions. Under large chiral parameters, the structure selectively achieves broadband anti-reflection for LCP waves, while consistently reflecting RCP waves across the bandwidth. This unique spin-dependent broadband anti-reflection results from significant phase delays between RCP and LCP waves, a feature not achievable by non-chiral, time-varying multilayer structures. Additionally, the proposed structure allows impedance matching between chiral and non-chiral dielectric spatial-temporal slabs in finite regions under small chiral parameters. These findings offer promising avenues for advanced wave manipulation in chiral metamaterials, with potential applications in broadband absorbers, filters, and quantum information processing systems.