Magnetic properties of the Pb[Cu(SO4)(OH)(2)] natural single crystal were investigated by magnetization measurements and compared in the low temperature region with the specific heat measurements. In the low temperature region in this quasi-one-dimensional Heisenberg system a phase transition to the long-range antiferromagnetic order is observed probably due to interchain interactions. The temperature dependence of susceptibility with a maximum at low temperatures, characteristic of low-dimensional anti ferromagnets, indicates a spin-singlet ground state separated from the excited triplet state by an energy gap.