We investigate a surface-mounted electrode geometry for miniature linear radio frequency Paul ion traps. The electrodes reside in a single plane on a substrate, and the pseudopotential minimum of the trap is located above the substrate at a distance on order of the electrodes lateral extent or separation. This architecture provides the possibility to apply standard microfabrication principles to the construction of multiplexed ion traps, which may be of particular importance in light of recent proposals for large-scale quantum computation based on individual trapped ions.