We present the outcomes of a Chandra X-Ray Observatory snapshot study of five nearby Herbig Ae/Be (HAeBe) stars that are kinematically linked with the Oph-Sco-Cen association (OSCA). Optical photometric and spectroscopic follow-up was conducted for the HD 104237 field. The principal result is the discovery of a compact group of pre-main-sequence (PMS) stars associated with HD 104237 and its codistant, comoving B9 neighbor Chamaeleontis AB. We name the group after the most massive member. The group has five confirmed stellar systems ranging from spectral type B9 to M5, including a remarkably high degree of multiplicity for HD 104237 itself. The HD 104237 system is at least a quintet, with four low-mass PMS companions in nonhierarchical orbits within a projected separation of 1500 AU of the HAeBe primary. Two of the low-mass members of the group are actively accreting classical T Tauri stars. The Chandra observations also increase the census of companions for two of the other four HAeBe stars, HD 141569 and HD 150193, and identify several additional new members of the OSCA. We discuss this work in light of several theoretical issues: the origin of X-rays from HAeBe stars; the uneventful dynamical history of the high-multiplicity HD 104237 system; and the origin of the Cha group and other OSCA outlying groups in the context of turbulent giant molecular clouds. Together with the similar η Cha cluster, we paint a portrait of sparse stellar clusters dominated by intermediate-mass stars 5-10 Myr after their formation.