The era of Big Data requires nanophotonic chips to have large information processing capacity. Multiple frequency on-chip nanophotonic devices are highly desirable for density integration, but such devices are more susceptible to structural imperfection because of their nano-scale. Topological photonics provides a robust platform for next-generation nanophotonic chips. Here we give an experimental report of an on-chip nanophotonic topological rainbow realized by employing a translational deformation freedom as a synthetic dimension. The topological rainbow can separate, slow, and trap topological photonic states of different frequencies into different positions. A homemade scattering scanning near-field optical microscope with high resolution is introduced to directly measure the topological rainbow effect of the silicon-based photonic chip. The topological rainbow based on synthetic dimension have no restrictions for optical lattice types, symmetries, materials, wavelength band, and is easy for on-chip integration. This work builds a bridge between silicon chip technologies and topological photonics.