Fused silica glass is the preferred material for applications which require long-term chemical and mechanical stability as well as excellent optical properties. The manufacturing of complex hollow microstructures within transparent fused silica glass is of particular interest for, among others, the miniaturization of chemical synthesis towards more versatile, configurable and environmentally friendly flow-through chemistry as well as high-quality optical waveguides or capillaries. However, microstructuring of such complex three-dimensional structures in glass has proven evasive due to its high thermal and chemical stability as well as mechanical hardness. Here we present an approach for the generation of hollow microstructures in fused silica glass with high precision and freedom of three-dimensional designs. The process combines the concept of sacrificial template replication with a room-temperature molding process for fused silica glass. The fabricated glass chips are versatile tools for, among other, the advance of miniaturization in chemical synthesis on chip.