  A class of models of dark sectors consider new very weak interaction between
the ordinary and dark matter transmitted by U'(1) gauge bosons A' (dark
photons) mixing with our photons. If such A's exist, they could be searched for
in a light-shining-through-a-wall experiment with a high energy electron beam
from the CERN SPS. The proposed search scheme suggests detection of the e+e-
pairs produced in the A' -> e+e- decay with a very small opening angle.
Coordinate chambers based on the thin-wall drift tubes with a minimal material
budget and a two-hit resolution for e+ and e- tracks separated by more than 0.5
mm are considered as an option for detecting such pairs.
