A neutron multiplicity counter assembly has been constructed to enable a search for superheavy elements in natural samples and in accelerator targets. The detector consists of twenty 3He counters placed in a paraffin moderator. These counters surround a central sample cavity with a capacity of about 20 1, capable of accomodating samples up to 100 kg in weight, depending on the density. A particular feature of this counter is its relative insensitivity to gamma rays. The efficiency for detecting a single neutron is ≈ 30%. An estimate of v, the number of neutrons emitted per fission in a sample, may be obtained from the observed multiplicity distribution P(n), where n is the number of neutron counts in an event. More accurate values of v may be obtained for small, isolated samples of spontaneously fissioning isotopes, where the neutron counters may be gated by a fission fragment detector. The design of the counter and an analysis of its properties are presented.