Control over core structure is much more challenging than that over shell structure in core-shell silver nanoclusters. Herein, two isostructural chalcogen-mediated [Ag(6)Z(4)@Ag-36] (Z = S or Se) nanoclusters (SD/Ag42a and SD/Ag42b) caging tetrahedral [Ag(6)Z(4)] as cores were synthesized by introducing Ph3CSH or Ph3PSe as slow-release source of S2- or Se2-, respectively, and characterized by single-crystal X-ray diffraction (SCXRD). As compared to the previously reported [AgS4@Ag-36] cluster (Ag37), we found that introducing additional S2- or Se2- ions can effectively enlarge the inner core from tetrahedral AgS4 to Ag(6)Z(4), which is a regular octahedron of silver with four Z(2-) capping on one tetrahedral set of four faces. More interestingly, the molecular enantiomers of SD/Ag42a and SD/Ag42b segregate into different crystals (P2(1)2(1)2(1)), while those of Ag37 form racemic crystals (I4(1)/acd). The larger Ag(6)Z(4) core in Ag42 clusters also extends their emission to the near-infrared region (similar to 760 nm). The study confirms that chalcogenide can enlarge the nuclearity of nanoclusters by altering the inner core structure and affords a new strategy to synthesize chiral core-shell silver nanoclusters of higher-order in controlled fashion.