A radiochemical experiment has been performed in the Gran Sasso Underground Laboratory to measure the fast neutron flux in the environment of the GALLEX Solar Neutrino experiment. Neutrons are detected via the reaction n + 4 0 Ca → 3 7 Ar + 4 He and the calcium target is in the form of 470 l of a calcium nitrate solution. It is found that only 0.44 ± 0.24 3 7 Ar atom is produced per day. This leads to a neutron flux above 2.5 MeV of (0.9 ± 0.6) 10 - 7 cm - 2 s - 1 . An evaluation of the neutron induced background in the GALLEX experiment is done using a Monte Carlo simulation program. The value obtained, 0.15 ± 0.10 SNU, is about 0.2% of the signal measured by GALLEX.