  The even-denominator fractional quantum Hall states (FQHSs) in half-filled
Landau levels are generally believed to host non-Abelian quasiparticles and be
of potential use in topological quantum computing. Of particular interest is
the competition and interplay between the even-denominator FQHSs and other
ground states, such as anisotropic phases and composite fermion Fermi seas.
Here we report the observation of an even-denominator fractional quantum Hall
state with highly-anisotropic in-plane transport coefficients at Landau level
filling factor $\nu=3/2$. We observe this state in an ultra-high-quality GaAs
two-dimensional hole system when a large in-plane magnetic field is applied. By
increasing the in-plane field, we observe a sharp transition from an isotropic
composite fermion Fermi sea to an anisotropic even-denominator FQHS. Our data
and calculations suggest that a unique feature of two-dimensional holes, namely
the coupling between heavy-hole and light-hole states, combines different
orbital components in the wavefunction of one Landau level, and leads to the
emergence of a highly-anisotropic even-denominator fractional quantum Hall
state. Our results demonstrate that the GaAs two-dimensional hole system is a
unique platform for the exploration of exotic, many-body ground states.
