We study deuterium fractionation in two massive starless/early-stage cores C1-N and C1-S in Infrared Dark Cloud (IRDC) G028.37+00.07, first identified by Tan et al. (2013) with ALMA. Line emission from multiple transitions of $rm N_2H^+$ and $rm N_2D^+$ were observed with the ALMA, CARMA, SMA, JCMT, NRO 45m and IRAM 30m telescopes. By simultaneously fitting the spectra, we estimate the excitation conditions and deuterium fraction, $D_{rm frac}^{rm N_2H^+} equiv [rm N_2D^+]/[N_2H^+]$, with values of $D_{rm frac}^{rm N_2H^+} simeq 0.2$--$0.7$, several orders of magnitude above the cosmic [D]/[H] ratio. Additional observations of o-H$_2$D$^+$ are also presented that help constrain the ortho-to-para ratio of $rm H_2$, which is a key quantity affecting the degree of deuteration. We then present chemodynamical modeling of the two cores, exploring especially the implications for the collapse rate relative to free-fall, $alpha_{rm ff}$. In order to reach the high level of observed deuteration of $rm N_2H^+$, we find that the most likely evolutionary history of the cores involves collapse at a relatively slow rate, $lesssim1/10$th of free-fall.
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