A novel approach to achieving robust single-spatial-mode operation of cladding-pumped fiber lasers with multimode cores is reported. The approach is based on the use of a fiber geometry in which the core has a helical trajectory within the inner cladding to suppress laser oscillation on higher-order modes. In a preliminary proof-of-principle study, efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser with a 30 microm diameter core and a numerical aperture of 0.087 has been demonstrated. The laser yielded 60.4 W of output at 1043 nm in a beam with M2 < 1.4 for 92.6 W launched pump power from a diode stack at 976 nm. The slope efficiency at pump powers well above threshold was approximately 84%, which compares favorably with the slope efficiencies achievable with conventional straight-core Yb-doped double-clad fiber lasers.