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We report the discovery of superconductivity with a maximum T_c of 1.28 K in Br-doped (PbSe)_1:12(TaSe₂), which is a new misfit compound consisting of alternating layers of distorted rocksalt PbSe and dichalcogenide TaSe₂. The Br-doping is required for the formation of this misfit compound and superconductivity can be tuned by changing Br content. The large anisotropic parameters in both resistivity and upper critical field H_c2 are found. The estimated c-axis coherence length of 6.3 nm is larger than the c-axis lattice constant, which implies that this compound is an anisotropic three-dimensional superconductor. The Hall coefficient measurements suggest that the charge transport is dominated by the hole-type charge carrier and there is a charge transfer from the PbSe layer to the conducting TaSe₂ layer. The small normalized specific heat jump and electron-phonon coupling constant of 0.61 indicate that Br-doped (PbSe)1:12(TaSe2) should be a weak-coupling BCS superconductor. The point-contact Andreev reflection spectroscopy is also studied.