The mechanical properties of biological cells have long been considered as inherent marker of biological function and disease. However, the screening and active sorting of heterogeneous populations based on serial single-cell mechanical measurements has not been demonstrated. Here we present a novel monolithic glass chip for combined fluorescence detection and mechanical phenotyping using an optical stretcher. A new design and manufacturing process, involving the bonding of two asymmetrically etched glass plates, combines exact optical fiber alignment, low laser damage threshold and high imaging quality with the possibility of several microfluidic inlet and outlet channels. We show the utility of such a custom-built optical stretcher glass chip by measuring and sorting single cells in a heterogeneous population based on their different mechanical properties and verify sorting accuracy by simultaneous fluorescence detection. This offers new possibilities of exact characterization and sorting of small populations based on rheological properties for biological and biomedical applications.