  Single-component fractional quantum Hall states (FQHSs) at even-denominator
filling factors may host non-Abelian quasiparticles that are considered to be
building blocks of topological quantum computers. Such states, however, are
rarely observed in the lowest-energy Landau level, namely at filling factors
$\nu<1$. Here we report evidence for an even-denominator FQHS at $\nu=1/4$ in
ultra-high-quality two-dimensional hole systems confined to modulation-doped
GaAs quantum wells. We observe a deep minimum in the longitudinal resistance at
$\nu=1/4$, superimposed on a highly insulating background, suggesting a close
competition between the $\nu=1/4$ FQHS and the magnetic-field-induced, pinned
Wigner solid states. Our experimental observations are consistent with the very
recent theoretical calculations which predict that substantial Landau level
mixing, caused by the large hole effective mass, can induce composite fermion
pairing and lead to a non-Abelian FQHS at $\nu=1/4$. Our results demonstrate
that Landau level mixing can provide a very potent means for tuning the
interaction between composite fermions and creating new non-Abelian FQHSs.
