Single-cell analysis tools have made substantial advances in characterizing genomic heterogeneity; however, tools for measuring phenotypic heterogeneity have lagged due to the increased difficulty of handling live biology. Here, we report a single-cell phenotyping tool capable of measuring image-based clonal properties at scales approaching 100,000 clones per experiment. These advances are achieved by exploiting a previously unidentified flow regime in ladder microfluidic networks that, under appropriate conditions, yield a mathematically perfect cell trap. Machine learning and computer vision tools are used to control the imaging hardware and analyze the cellular phenotypic parameters within these images. Using this platform, we quantified the responses of tens of thousands of single cell–derived acute myeloid leukemia (AML) clones to targeted therapy, identifying rare resistance and morphological phenotypes at frequencies down to 0.05%. This approach can be extended to higher-level cellular architectures such as cell pairs and organoids and on-chip live-cell fluorescence assays.