This paper introduces a concept that allows the creation of low-resistance composites using a network of compliant conductive aggregate units, connected through contact, embedded within the composite. Due to the straight-forward fabrication method of the aggregate, conductive composites can be created in nearly arbitrary shapes and sizes, with a lower bound near the length scale of the conductive cell used in the aggregate. The described instantiation involves aggregate cells that are approximately spherical copper coils-of-coils within a polymeric matrix, but the concept can be implemented with a wide range of conductor elements, cell geometries, and matrix materials due to its lack of reliance on specific material chemistries. The aggregate cell network provides a conductive pathway that can have orders of magnitude lower resistance than that of the matrix material--from 10(12) ohm-cm (approx.) for pure silicone rubber to as low as 1 ohm-cm for the silicone/copper composite at room temperature for the presented example. After describing the basic concept and key factors involved in its success, three methods of implementing the aggregate into a matrix are then addressed--unjammed packing, jammed packing, and pre-stressed jammed packing--with an analysis of the tradeoffs between increased stiffness and improved resistivity.