A large number of Grids have been developed worldwide. Despite being mostly based on the same underlying middleware, the Globus Toolkit, they are generally not inter-operable for a variety of reasons. We present a method of federating those disparate grids which are based on the Globus Toolkit, together with a concrete example of interfacing the LHC Computing Grid (LCG) with HEPGrid. HEPGrid consists of shared resources, at several Canadian research institutes, which are exposed via Globus gatekeepers, and makes use of Condor-G for resource advertisement, matchmaking and job submission. An LCG Computing Element (CE) based at the TRIUMF Laboratory hosts a HEPGrid User Interface (UI) that is contained within a custom JobManager. This JobManager appears in the LCG information system as a normal CE publishing an aggregation of the HEPGrid resources. The interface interprets the incoming job in terms of HEPGrid UI usage, submits it onto HEPGrid, and implements the JobManager 'poll' and 'remove' methods, thus enabling monitoring and control across the grids. In this way non-LCG resources are integrated into LCG, without the need for LCG middleware on those resources. The same method can be used to create interfaces between other grids, with the details of the child-Grid being fully abstracted into the interface layer. The LCG-HEPGrid interface is operational, and has been used to federate 1300 CPU's at 4 sites into LCG for the ATLAS Data Challenge (DC2).