Colloidal Ag(In,Ga)S2nanocrystals (AIGS NCs) with the band gap tunability by their size and composition within visible range have garnered surging interest. High absorption cross-section and narrow emission linewidth of AIGS NCs make them ideally suited to address the challenges of Cd-free NCs in wide-ranging photonic applications. However, AIGS NCs have shown relatively underwhelming photoluminescence quantum yield (PL QY) to date, primarily because coherent heteroepitaxy has not been realized. Here, we report the heteroepitaxy for AIGS-AgGaS2(AIGS-AGS) core-shell NCs bearing near-unity PL QYs in almost full visible range (460 to 620 nm) and enhanced photochemical stability. Key to the successful growth of AIGS-AGS NCs is the use of the Ag-S-Ga(OA)2complex, which complements the reactivities among cations for both homogeneous AIGS cores in various compositions and uniform AGS shell growth. The heteroepitaxy between AIGS and AGS results in the Type I heterojunction that effectively confines charge carriers within the emissive core without optically active interfacial defects. AIGS-AGS NCs show higher extinction coefficient and narrower spectral linewidth compared to state-of-the-art heavy metal-free NCs, prompting their immediate use in practicable applications including displays and luminescent solar concentrators (LSCs).