  Fractional quantum Hall states (FQHSs) exemplify exotic phases of
low-disorder two-dimensional (2D) electron systems when electron-electron
interaction dominates over the thermal and kinetic energies. Particularly
intriguing among the FQHSs are those observed at even-denominator Landau level
filling factors, as their quasi-particles are generally believed to obey
non-Abelian statistics and be of potential use in topological quantum
computing. Such states, however, are very rare and fragile, and are typically
observed in the excited Landau level of 2D electron systems with the lowest
amount of disorder. Here we report the observation of a new and unexpected
even-denominator FQHS at filling factor {\nu} = 3/4 in a GaAs 2D hole system
with an exceptionally high quality (mobility). Our magneto-transport
measurements reveal a strong minimum in the longitudinal resistance at {\nu} =
3/4, accompanied by a developing Hall plateau centered at (h/e2)/(3/4). This
even-denominator FQHS is very unusual as it is observed in the lowest Landau
level and in a 2D hole system. While its origin is unclear, it is likely a
non-Abelian state, emerging from the residual interaction between composite
fermions.
