  A neutron counter designed for assay of radioactive materials has been
adapted for beam experiments at TUNL. The cylindrical geometry and 60% maximum
efficiency make it well suited for ($\gamma,n$) cross-section measurements near
the neutron emission threshold. A high precision characterization of the
counter has been made using neutrons from several sources. Using a combination
of measurements and simulations, the absolute detection efficiency of the
neutron counter was determined to an accuracy of $\pm$ 3% in the neutron energy
range between 0.1 and 1 MeV. It is shown that this efficiency characterization
is generally valid for a wide range of targets.
