  We describe an approach to optically trapping small, chemically stable
molecules at cryogenic temperatures by buffer-gas loading a deep optical dipole
trap. The ~10 K trap depth will be produced by a tightly-focused, 1064-nm
cavity capable of reaching intensities of hundreds of GW/cm$^2$. Molecules will
be directly buffer-gas loaded into the trap using a helium buffer gas at 1.5 K.
The very far-off-resonant, quasielectrostatic trapping mechanism is insensitive
to a molecule's internal state, energy level structure, and its electric and
magnetic dipole moment. Here, we theoretically investigate the trapping and
loading dynamics, as well as the heating and loss rates, and conclude that
$10^4$-$10^6$ molecules are likely to be trapped. Our trap would open new
possibilities in molecular spectroscopy, studies of cold chemical reactions,
and precision measurement, amongst other fields of physics.
