  The Cold molecule Nuclear Time-Reversal EXperiment (CeNTREX) is a new effort
aiming for a significant increase in sensitivity over the best present upper
bounds on the strength of hadronic time reversal ($T$) violating fundamental
interactions. The experimental signature will be shifts in nuclear magnetic
resonance frequencies of $^{205}$Tl in electrically-polarized thallium fluoride
(TlF) molecules. Here we describe the motivation for studying these
$T$-violating interactions and for using TlF to do so. To achieve higher
sensitivity than earlier searches for $T$-violation in TlF, CeNTREX uses a
cryogenic molecular beam source, optical state preparation and detection, and
modern methods of coherent quantum state manipulation. Details of the
measurement scheme and the current state of the apparatus are presented, with
quantitative measurements of the TlF beam. Finally, the estimated sensitivity
and methods to control systematic errors are discussed.
