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PbCu(SeO4)(OH)2, the selenate sibling of the mineral linarite, was synthesized hydrothermally, investigated in measurements of magnetization M, specific heat Cp and dielectric permittivity ε, and analyzed within density functional theory formalism. This quasi-one-dimensional compound evidences formation of a short-range correlation regime at T* ~ 8 K and experiences a long-range magnetic order at TN = 4.3 K. A magnetization saturation of approximately 1 µB is reached at µ0Hflip ~ 16 T preceded by a jump at µ0Hflop = 2.4 T. Additionally, there are multiple indicators of the formation of an additional electrically active phase above the Neel temperature, which suggests that PbCu(SeO4)(OH)2 is a multiferroic system.