Generalized vector vortex light beams possess spatially variant polarization states, and higher-order Poincaré spheres represent a powerful analytical tool for analyzing these intriguing and complicated optical fields. For the generation of these vortex beams, a range of different methods have been explored, with an increasing emphasis placed on compact, integrated devices. Here, we demonstrate via numerical simulation, for the first time, an on-chip light emitter that allows for the controllable generation of all points on a first-order Poincaré sphere (FOPS). The FOPS beam generator consists of a waveguide-coupled, nanostructured Si microring resonator that converts two guided, coherent light waves into freely propagating output light. By matching their whispering gallery modes with the nanostructures, the fundamental TE (transverse electric) and TM (transverse magnetic) input modes produce radial and azimuthal polarizations, respectively. These two linear polarizations can form a pair of eigenstates for the FOPS. Consequently, tuning the phase contrast and the intensity ratio of these two coherent inputs allows for the generation of an arbitrary point on the FOPS. This result indicates a new way for on-chip vector vortex beam generation, which may be applied for integrated optical tweezers and high-capacity optical communications.