Charginos and neutralinos are searched for in the data collected by the ALEPH experiment at LEP for centre-of-mass energies up to 209 GeV. The negative result of these searches is combined with those from searches for sleptons and Higgs bosons to derive an absolute lower limit of 43.1 GeV/c2 on the mass of the lightest supersymmetric particle (LSP), assumed to be the lightest neutralino. This limit is obtained in the framework of the MSSM with R-parity conservation and with gaugino and sfermion mass unification at the GUT scale and assuming no mixing in the stau sector. The LSP limit degrades only slightly to 42.4 GeV/c2 if stau mixing is considered. Within the more constrained framework of minimal supergravity, the limit is 50 GeV/c2.