  The hydrogen molecule has become a test ground for quantum electrodynamical
calculations in molecules. Expanding beyond studies on stable hydrogenic
species to the heavier radioactive tritium-bearing molecules, we report on a
measurement of the fundamental T$_2$ vibrational splitting $(v= 0 \rightarrow
1)$ for $J=0-5$ rotational levels. Precision frequency metrology is performed
with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental
uncertainty of $10-12$~MHz, where sub-Doppler saturation features are exploited
for the strongest transition. The achieved accuracy corresponds to a fifty-fold
improvement over a previous measurement, and allows for the extraction of
relativistic and QED contributions to T$_2$ transition energies.
