A test of parity-conserving, time-reversal non-invariance (PC TRNI) has been performed in 5.9 MeV polarized neutron transmission through nuclear spin aligned holmium. The experiment searches for the T-violating five-fold correlation via a double modulation technique - flipping the neutron spin while rotating the alignment axis of the holmium. Relative cross sections for spin-up and spin-down neutrons are found to be equal to within $1.2 times 10^{-5}$ (80% confidence). This is a two order of magnitude improvement compared to traditional detailed balance studies of time reversal, and represents the most precise test of PC TRNI in a dynamical process.