  A significant fraction of binary neutron star mergers occur in star-forming
galaxies where the UV-optical and soft X-ray afterglow emission from the
relativistic jet may be absorbed by dust and re-emitted at longer wavelengths.
We show that, for mergers occurring in gas-rich environment (n_H > 0.5 cm^{-3}
at a few to tens of pc) and when the viewing angle is less than about 30
degrees, the emission from heated dust should be detectable by James Webb Space
Telescope (JWST), with a detection rate of the order once per year. The spatial
separation between the dust emission and the merger site is a few to 10
milli-arcsecs (for a source distance of 150 Mpc), which may be astrometrically
resolved by JWST for sufficiently high signal-noise-ratio detections. Measuring
the superluminal apparent speed of the flux centroid directly gives the orbital
inclination of the merger, which can be combined with gravitational wave data
to measure the Hubble constant. For a line of sight within the jet opening
angle, the dust echoes are much brighter and may contaminate the search for
kilonova candidates from short gamma-ray bursts, such as the case of GRB
130603B.
