Most existing reference-based distributed object systems include some kind of acyclic garbage collection, but fail to provide acceptable collection of cyclic garbage. Those that do provide such GC currently suffer from one or more problems: synchronous operation, the need for expensive global consensus or termination algorithms, susceptibility to communication problems, or an algorithm that does not scale. We present a simple, complete, fault-tolerant, asynchronous extension to the (acyclic) cleanup protocol of the SSP Chains system. This extension is scalable, consumes few resources, and could easily be adapted to work in other reference-based distributed object systems---rendering them usable for very large-scale applications.