  A novel chiral electron-hole (CEH) pairing mechanism is proposed to account
for non-BCS superconductivity. In contrast to BCS Cooper pairs, CEH pairs
exhibit a pronounced affinity to antiferromagnetism for superconductivity. The
gap equations derived from this new microscopic mechanism are analyzed for both
s- and d-wave superconductivity, revealing marked departures from the BCS
theory. Unsurprisingly, CEH naturally describes superconductivity in
strongly-correlated systems, necessitating an exceedingly large coupling
parameter ($\lambda>1$ for s-wave and $\lambda>\pi/2$ for d-wave) to be
efficacious. The new mechanism provides a better understanding of various
non-BCS features, especially in cuprate and iron-based superconductors. In
particular, CEH, through quantitative comparison with experimental data, shows
promise in solving long-standing puzzles such as the unexpectedly large
gap-to-critical-temperature ratio $\Delta_0/T_c$, the lack of gap closure at
$T_c$, superconducting phase diagrams, and a non-zero
heat-capacity-to-temperature ratio $C/T$ at $T=0$ (i.e., the ``anomalous linear
term''), along with its quadratic behavior near $T=0$ for d-wave cuprates.
