Polycrystalline (PbS)1.14(TaS2)2, a misfit layer sulfide, was used as cathodic material for lithium secondary battery. One molar LiClO4 in propylene carbonate (PC) was used as electrolyte. The cell could be galvanostatic discharged down to x = 4.6 [Li(x)(PbS)1.14(TaS2)2] when the current density was 65 muA cm-2 and the cell was cycled more than 100 times between 3.5 and 1.5 V at a current density of 260 muA cm-2. Lattice expansion increased linearly with lithium content and was less than that reported for the Li/TaS2 system. Chemical diffusion coefficients were determined by a modified version of the galvanostatic intermittent titration technique and they were fairly constant in the composition range 0.2 < x < 1, and an average value of 8.1 x 10(-11) cm2 s-1 was calculated. Sodium intercalation was also accomplished, but the uptake of this ion resulting in a significant lattice expansion compared with that observed for lithium ions. Moreover, a similar dependence of the sodium chemical diffusion coefficient on the composition was observed with an average value of 1.4 x 10(-10) cm2 s-1, somewhat higher than that of lithium ion. We believe that differences in lattice expansion may be responsible for the differences found in the chemical diffusivity values.