Circularly polarized light (CPL) exerts a force of different magnitude on left- and right-handed enantiomers, an effect that could be exploited for chiral resolution of chemical compounds as well as controlled assembly of chiral nanostructures. However, enantioselective optical forces are challenging to control and quantify because their magnitude is extremely small (sub-piconewton) and varies in space with sub-micrometre resolution. Here, we report a technique to both strengthen and visualize these forces, using a chiral atomic force microscope probe coupled to a plasmonic optical tweezer. Illumination of the plasmonic tweezer with CPL exerts a force on the microscope tip that depends on the handedness of the light and the tip. In particular, for a left-handed chiral tip, transverse forces are attractive with left-CPL and repulsive with right-CPL. Additionally, total force differences between opposite-handed specimens exceed 10 pN. The microscope tip can map chiral forces with 2 nm lateral resolution, revealing a distinct spatial distribution of forces for each handedness.