Chain reactions are characterized by initiation, propagation and termination, are stochastic at microscopic scales and underlie vital chemical (e.g. combustion engines), nuclear and biotechnological (e.g. polymerase chain reaction) applications.1-5 At macroscopic scales, chain reactions are deterministic and limited to applications for entertainment and art such as falling domino and Rube Goldberg machines. Appositely, the microfluidic lab-on-a-chips (also called a micro total analysis system),6,7 was envisioned as an integrated chip, akin to microelectronic integrated circuits, yet in practice remain dependent on cumbersome peripherals, connections, and a computer for automation.8-11 Capillary microfluidics integrate energy supply and flow control onto a single chip by using capillary phenomena, but programmability remains rudimentary with at most a handful (eight) operations possible.12-19 Here we introduce the microfluidic chain reaction (MCR) as the conditional, structurally programmed propagation of capillary flow events. Monolithic chips integrating a MCR are 3D printed, and powered by the free-energy of a paper pump, autonomously execute liquid handling algorithms step-by-step. With MCR, we automated (i) the sequential release of 300 aliquots across chained, interconnected chips, (ii) a protocol for SARS-CoV-2 antibodies detection in saliva, and (iii) a thrombin generation assay by continuous subsampling and analysis of coagulation-activated plasma with parallel operations including timers, iterative cycles of synchronous flow and stop-flow operations. MCRs are untethered from and unencumbered by peripherals, encode programs structurally in situ, and can form frugal, versatile, bona fide lab-on-a-chip with wide-ranging applications in liquid handling and point-of-care diagnostics.