  Infrared Dark Clouds (IRDCs) are cold, dense regions that are usually found
within Giant Molecular Clouds (GMCs). Ongoing star formation within IRDCs is
typically still deeply embedded within the surrounding molecular gas.
Characterising the properties of relatively quiescent IRDCs may therefore help
us to understand the earliest phases of the star formation process. Studies of
local molecular clouds have revealed that deuterated species are enhanced in
the earliest phases of star formation. In this paper we test this towards IRDC
G035.39-00.33. We present an 80 arcsec by 140 arcsec map of the J=2-1
transition of N2D+, obtained with the IRAM-30m telescope. We find that N2D+ is
widespread throughout G035.39-00.33. Complementary observations of N2H+(1-0)
are used to estimate the deuterium fraction, N(N2D+)/N(N2H+). We report a mean
deuterium fraction of 0.04+-0.01, with a maximum of 0.09+-0.02. The mean
deuterium fraction is ~3 orders of magnitude greater than the interstellar
[D]/[H] ratio. High angular resolution observations are required to exclude
beam dilution effects of compact deuterated cores. Using chemical modelling, we
find that the average observed values of the deuterium fraction are in
agreement with an equilibrium deuterium fraction, given the general properties
of the cloud. This implies that the IRDC is at least ~3Myr old, which is ~8
times longer than the mean free-fall time of the observed deuterated region.
