In　a　recent　paper,　we　developed　a　novel　quantized　kernel　least　mean　square　algorithm,　in　which　the　input　space　is　quantized　(partitioned　into　smaller　regions)　and　the　network　size　is　upper　bounded　by　the　quantization　codebook　size　(number　of　the　regions).　In　this　brief,　we　propose　the　quantized　kernel　least　squares　regression,　and　derive　the　optimal　solution.　By　incorporating　a　simple　online　vector　quantization　method,　we　derive　a　recursive　algorithm　to　update　the　solution,　namely　the　quantized　kernel　recursive　least　squares　algorithm.　The　good　performance　of　the　new　algorithm　is　demonstrated　by　Monte　Carlo　simulations.