We report on a narrow-linewidth distributed-feedback quantum cascade laser at 8.6 μm that is optical-feedback locked to a high-finesse V-shaped cavity. The spectral purity of the quantum cascade laser is fully characterized using a high-sensitivity optical frequency discriminator, leading to a 1 ms linewidth of less than 4 kHz and a minimum laser frequency noise spectral density as low as 0.01 Hz2/Hz for Fourier frequencies larger than 100 kHz. The cumulative standard deviation of the laser intensity is better than 0.1% over an integration bandwidth from 2 Hz to 100 MHz.