In this paper we present a novel two-stage method to realize a lightweight but very capable hardware implementation of a Learning Classifier System for on-chip learning. Learning Classifier Systems (LCS) allow taking good run-time decisions, but current hardware implementations are either large or have limited learning capabilities. In this work, we combine the capabilities of a software-based LCS, the XCS, with a lightweight hardware implementation, the LCT, retaining the benefits of both. We compare our method with other LCS implementations using the multiplexer problem and evaluate it with two chip-related problems, run-time task allocation and SoC component parameterization. In all three problem sets, we find that the learning and self-adaptation capabilities are comparable to a full-fledged system, but with the added benefits of a lightweight hardware implementation, namely small area size and quick response time. Given our work, autonomous chips based on Learning Classifier Systems become feasible.