  Presented here are results of simulations of neutron background performed for
a time projection chamber acting as a particle dark matter detector in an
underground laboratory. The investigated background includes neutrons from rock
and detector components, generated via spontaneous fission and (alpha, n)
reactions, as well as those due to cosmic-ray muons. Neutrons were propagated
to the sensitive volume of the detector and the nuclear recoil spectra were
calculated. Methods of neutron background suppression were also examined and
limitations to the sensitivity of a gaseous dark matter detector are discussed.
Results indicate that neutrons should not limit sensitivity to WIMP-nucleon
interactions down to a level of (1 - 3) x 10^{-8} pb in a 10 kg detector.
