Motor sequences are formed through the serial execution of different movements, but how nervous systems implement this process remains largely unknown. We determined the organizational principles governing how dirty fruit flies groom their bodies with sequential movements. Using genetically targeted activation of neural subsets, we drove distinct motor programs that clean individual body parts. This enabled competition experiments revealing that the motor programs are organized into a suppression hierarchy; motor programs that occur first suppress those that occur later. Cleaning one body part reduces the sensory drive to its motor program, which relieves suppression of the next movement, allowing the grooming sequence to progress down the hierarchy. A model featuring independently evoked cleaning movements activated in parallel, but selected serially through hierarchical suppression, was successful in reproducing the grooming sequence. This provides the first example of an innate motor sequence implemented by the prevailing model for generating human action sequences.