Context. High degrees of deuterium fractionation are commonly found in cold prestellar cores and in the envelopes around young protostars. As it brings strong constraints to chemical models, deuterium chemistry is often used to infer core history or molecule formation pathways. Whereas a large number of observations are available regarding interstellar deuterated stable molecules, relatively little is known about the deuteration of hydride radicals, as their fundamental rotational transitions are at high frequencies where the atmosphere is mostly opaque. Aims. Nitrogen hydride radicals are important species in nitrogen chemistry, as they are thought to be related to ammonia formation. Observations have shown that ammonia is strongly deuterated, with [NH2D]/[NH3] ~ 10%. Models predict similarly high [ND]/[NH] ratios, but so far only one observational determination of this ratio is available, towards the envelope of the protostar IRAS16293-2422. To test model predictions, we aim here to determine [ND]/[NH] in a dense, starless core. Methods. We observed NH and ND in 16293E with the HIFI spectrometer on board the Herschel Space Observatory as part of the CHESS guaranteed time key programme, and derived the abundances of these two species using a non local thermodynamic equilibrium radiative transfer model. Results. Both NH and ND are detected in the source, with ND in emission and NH in absorption against the continuum that arises from the cold dust emission. Our model shows, however, that the ND emission and the NH absorption originate from different layers in the cloud, as further evidenced by their different velocities. In the central region of the core, we can set a lower limit to the [ND]/[NH] ratio of ≳2%. This estimate is consistent with recent pure gas-phase models of nitrogen chemistry.