We propose and analyze theoretically a promising design of an optical trap for vacuum levitation of nanoparticles based on a one-dimensional (1D) silicon photonic crystal cavity (PhC). The considered cavity has a quadratically modulated width of the silicon wave guiding structure, leading to a calculated cavity quality factor of 8 × 105. An effective mode volume of approximately 0.16 μm3 having the optical field strongly confined outside the silicon structure enables optical confinement on nanoparticle in all three dimensions. The optical forces and particle-cavity optomechanical coupling are comprehensively analyzed for two sizes of silica nanoparticles (100 nm and 150 nm in diameter) and various mode detunings. The value of trapping stiffnesses in the microcavity is predicted to be 5 order of magnitudes higher than that reached for optimized optical tweezers, moreover the linear single photon coupling rate can reach MHz level which is 6 order magnitude larger than previously reported values for common bulk cavities. The theoretical results support optimistic prospects towards a compact chip for optical levitation in vacuum and cooling of translational mechanical degrees of motion for the silica nanoparticle of a diameter of 100 nm.