The performance characteristics of a plane parallel chamber were investigated on beams of slow muons and positrons, as well as on an electron beam from a 106Ru β source. The chamber was filled with CO2 or a gas mixture of Ar (30%) + CO2(70%) at atmospheric pressure. The amplitude spectra of charged particles and the efficiency of their detection were measured. The muon and positron momenta were ∼27 MeV/c. It was shown that the muon detection efficiency of the plane parallel chamber with a 1-mm gas gap and CO2 (100%) used as a working gas was as high as 99%, while that of the chamber with a 0.4-mm gas gap and a working gas mixture of Ar(30%) + CO2(70%) was 88%. This result, along with the detector's high response speed, allows the plane parallel chamber to be used as an active target being developed for a future experiment (FAMILON) on searching for neutrinoless muon decay with the release of a scalar Goldstone's boson (µ → eα).