  A high sensitivity search for a light \Ub{} by means of a positron beam
incident on a hydrogen target is proposed. We described a concept of the
experiment and two possible realizations. The projected result of this
experiment corresponds to an upper limit on the square of coupling constant $
|f_{_{eU}}|^2 = 3 \times 10^{-9}$ with a signal to noise ratio of five.
