The quest for less costly and more compact high-energy particle accelerators makes research on alternative acceleration mechanisms an important enterprise. From the multitude of suggested concepts, the photonic accelerator design by B. M. Cowan [Phys. Rev. ST Accel. Beams 11, 011301 (2008)] stands out by its distinct potential of creating an accelerator on a chip [Proposal E-163, SLAC (2001)]. Herein, electrons are accelerated by the axial electric field of a strongly confined optical mode of an air waveguide within a silicon-based three-dimensional photonic band-gap material. Using a combination of direct laser writing and silicon double inversion, we here present the first experimental realization of this complex structure. Optical spectroscopy provides unambiguous evidence for the existence of an accelerating waveguide mode with axial polarization.