In this Letter, we present a high extinction ratio and compact on-chip polarization beam splitter (PBS), based on an extreme skin-depth (eskid) waveguide. Subwavelengthscale gratings form an effectively anisotropic metamaterial cladding and introduce a large birefringence. The anisotropic dielectric perturbation of the metamaterial cladding suppresses the TE polarization extinction via exceptional coupling, while the large birefringence efficiently cross-couples the TM mode, thus reducing the coupling length. We demonstrated the eskid-PBS on a silicon-on-insulator platform and achieved an ultra-high extinction ratio PBS (≈60 dB for TE and ≈48 dB for TM) with a compact coupling length (≈14.5 µm). The insertion loss is also negligible (<0.6 dB). The bandwidth is >80 (30) nm for the TE (TM) extinction ratio >20 dB. Our ultra-high extinction ratio PBS is crucial in implementing efficient polarization diversity circuits, especially where a high degree of polarization distinguishability is necessary, such as photonic quantum information processing.