The search for a homologous template is a central and critical step in the repair of DNA breaks by homologous recombination. However, it is still unclear how the search process is carried out within a cell. Here, we image double-stranded break (DSB) repair in living E. coli growing in a microfluidic device and show that two segregated homologous sequences find each other less than 9 min after an induced DSB. To characterize the mechanisms of the search process, we use a new RecA fluorescent fusion that rapidly forms structures after DSBs. Initially, RecA forms a bright cluster at the site of the DNA damage and then extends to form a thin, flexible, and dynamic filament. Based on our observations, we propose a model where the 1D ssDNA-RecA filament stretches along the cell, and the homology search is mediated by diffusion of the repair template that can interact with any segment of the filament. This model reduces the complexity of the search from 3D to 2D and quantitatively predicts that genome-wide search for homology can be finished in minutes, in agreement with our measurements.