We report a smectic-A–smectic-C–smectic-C* (ACC*) multicritical point in mixtures of chiral DOBAMBC [p-(n-decyloxybenzylidene)-p-amino-(2-methyl-butyl)] cinnamate and achiral 10O.8 (4-decyloxybenzylidene-4-octylaniline). Studies of the phase diagram, tilt angle (θ), polarization (P), and helix pitch (p) indicate an ACC* Lifshitz point that can be described in terms of the extended Landau theory. Specifically, the T*AC and the maximum polarization (Pm) exhibit quadratic composition dependence while the helical pitch length (p=2π/q) varies linearly. Both q and Pm vanish discontinuously at the C-C* phase boundary revealing its first order nature, consistent with a possible Lifshitz point.