Many of the objects imaged by the forthcoming generation of astronomical surveys will overlap visually. These objects are known as blends. Distinguishing and characterizing blended light sources is a challenging task, as there is inherent ambiguity in the type, position, and properties of each source. We propose SMC-Deblender, a novel approach to probabilistic astronomical cataloging based on sequential Monte Carlo (SMC). Given an image, SMC-Deblender evaluates catalogs with various source counts by partitioning the SMC particles into blocks. With this technique, we demonstrate that SMC can be a viable alternative to existing deblending methods based on Markov chain Monte Carlo and variational inference. In experiments with ambiguous synthetic images of crowded starfields, SMC-Deblender accurately detects and deblends sources, a task which proves infeasible for Source Extractor, a widely used non-probabilistic cataloging program.