We report the coherent manipulation of internal states of neutral atoms in a magnetic microchip trap. Coherence lifetimes exceeding 1 s are observed with atoms at distances of 5-130 microm from the microchip surface. The coherence lifetime in the chip trap is independent of atom-surface distance within our measurement accuracy and agrees well with the results of similar measurements in macroscopic magnetic traps. Because of the absence of surface-induced decoherence, a miniaturized atomic clock with a relative stability in the 10(-13) range can be realized. For applications in quantum information processing, we propose to use microwave near fields in the proximity of chip wires to create potentials that depend on the internal state of the atoms.