In modern technicolor models, there exist very narrow spin-zero and spin-one neutral technihadrons---$pi^0_T$, $rho^0_T$ and $omega_T$---with masses of a few 100 GeV. The large coupling of $pi^0_T$ to $mu^+mu^-$, the direct coupling of $rho^0_T$ and $omega_T$ to the photon and $Z^0$, and the superb energy resolution of the First Muon Collider may make it possible to resolve these technihadrons and produce them at extraordinarily large rates.