The properties of a molecularly thin film of spherically symmetric molecules confined to a chemically heterogeneous slit-pore were investigated by Monte Carlo simulations in a grand mixed stress-strain ensemble. The slit-pore comprises two identical plane-parallel solid substrates, each of which consists of alternating strips of solid of two types: strongly adsorbing (width d _s ) and weakly adsorbing. Under favourable thermodynamic conditions the confined film consists of fluid bridges - that is, a high(er)-density fluid over the strongly attractive strip surrounded by a low(er)-density fluid supported by the (outer) weakly attractive strips. By misaligning the opposite substrates, bridge phases can be exposed to a shear strain s_x (0 ½, s_x the side length of the simulation cell) and the associated shear stress T_zx of (fluidic) bridge phases can be calculated from molecular expressions. The stress curve T_zx ( s_x ) is qualitatively similar to the one characteristic of solidlike films confined between atomically structured substrates in that the initial response to small shear strains is Hookean, and this is followed by an increasingly nonlinear regime up to the yield point where T_zx ( s_x ) assumes its maximum. We also investigated the influence of chemical corrugation c _r : = d _s /s_x on T_zx ( s_x ). With increasing c _r , yield strain and stress increase at first up to a maximum and decline thereafter. By employing the theory of corresponding states, T_zx ( s_x ) is renormalized by yield stress and strain such that the results can be represented uniquely by a master curve independent of any system-dependent parameters.