BTeV is a dedicated beauty and charm experiment proposed for the Fermilab Tevatron. The broad physics program envisaged for BTeV requires a trigger that is efficient for a wide variety of heavy-quark decays, including those to all-hadronic final states. To achieve this, we plan to trigger on evidence of detached vertices at the very first trigger level, taking advantage of fast-readout pixel detectors to facilitate fast pattern recognition. Simulations show that 100-to-1 rejection of light-quark background events can be achieved. at Level 1 using specialized track finding hardware, and that an additional factor of 10 to 100 in data reduction can be achieved using general purpose processor farms at Levels 2 and 3. This is adequate to allow data taking at luminosities of 2 x 10^32 cm^-2 s^-1.