Liquid chromatography at the chromatographic critical condition has drawn much attention as an attractive characterization method of block copolymers since it has been proposed that a part of a polymer chain becomes "chromatographically invisible" at this condition, which would permit the characterization of individual blocks. A critical condition for a polymer species has been commonly established by use of mixed-solvent systems. It is not easy, however, to reproduce the critical condition since the retention of polymers depends very sensitively on the solvent composition and purity. Furthermore, the preferential sorption of a component in a mixed solvent may cause an additional problem. Therefore, the use of a single solvent is highly desirable to improve the reproducibility as well as the repeatability. In this study, a single-solvent critical condition for polyisoprene was established with 1,4-dioxane and C18 bonded silica as the mobile and stationary phases, respectively. At this condition, the "chromatographic invisibility" of polystyrene-polyisoprene diblock copolymers was critically examined and it was found that a rigorous chromatographic invisibility was not achieved and the retention of the block copolymers was affected by the length of the blocks under the critical condition. Some other chromatographic applications using the single-solvent system are also reported.