We present a cooling method that should be generally applicable to atoms with narrow optical transitions. This technique uses velocity-selective pulses to drive atoms towards a zero-velocity dark state and then quenches the excited state to increase the cooling rate. We demonstrate this technique of quenched narrow-line cooling by reducing the 1D temperature of a sample of neutral
40Ca atoms. We cool selected velocities with the
1S0(4s2)3P1(4s4p) 657-nm intercombination line and quench with the
3P1(4s4p)1S0(4s5s) intercombination line at 553 nm, which increases the cooling rate eightfold. Limited only by available quenching laser power, we have transferred 18% of the atoms from our initial 2-mK velocity distribution and achieved temperatures as low as 4 \ensuremath{\mu}K, corresponding to a
vrms of 2.8 cm/s or 2 recoils at 657 nm. This cooling technique, which is closely related to Raman cooling, can be extended to three dimensions.