We describe a modular apparatus for use in parity-violation measurements in epithermal neutron-nucleus resonances with high instantaneous neutron fluxes at the Manuel Lujan Jr. Neutron Scattering Center at Los Alamos National Laboratory. This apparatus is designed to conduct high-precision measurements of the parity-odd transmission asymmetry of longitudinally polarized neutrons through targets containing nuclei with p-wave neutron-nucleus resonances in the 0.1-10 eV energy regime and to accommodate a future search for time reversal violation in polarized neutron transmission through polarized nuclear targets. The apparatus consists of an adjustable neutron and gamma collimation system, a (^3)He-$^{4}$He ion chamber neutron flux monitor, two identical cryostats for target cooling, an adiabatic eV-neutron spin flipper, a near-unit efficiency (^6)Li-(^{7})Li scintillation detector operated in current mode, a flexible CAEN data acquisition system, and a neutron spin filter based on spin-exchange optical pumping of $^{3}$He gas. We describe the features of the apparatus design devoted to the suppression of systematic errors in parity-odd asymmetry measurements. We describe the configuration of the apparatus used to conduct a precision measurement of parity violation at the 0.7 eV p-wave resonance in $^{139}$La which employs two identical $^{139}$La targets, one to polarize the beam on the p-wave resonance using the weak interaction and one to analyze the polarization.
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