A new silicon based waveguide with full CMOS compatibility is developed to fabricate an on-chip Bragg cladding waveguide that has an oxide core surrounded by a high index contrast cladding layers. The cladding consists of several dielectric bilayers, where each bilayer consists of a high index-contrast pair of layers of Si and Si3N4. This new waveguide guides light based on omnidirectional reflection, reflecting light at any angle or polarization back into the core. Its fabrication is fully compatible with current microelectronics processes. In principle, a core of any low-index material can be realized with our novel structure, including air. Potential applications include tight turning radii, high power transmission, and dispersion compensation.