We demonstrate an atom interferometer that uses a laser-cooled continuous beam of $^{87}$Rb atoms having velocities of 10--20 m/s. With spatially separated Raman beams to coherently manipulate the atomic wave packets, Mach--Zehnder interference fringes are observed at an interference distance of 2L = 19 mm. The apparatus operates within a small enclosed area of 0.07 mm$^2$ at a bandwidth of 190 Hz with a deduced sensitivity of $7.8times10^{-5}$ rad/s/$sqrt{{Hz}}$ for rotations. Using a low-velocity continuous atomic source in an atom interferometer enables high sampling rates and bandwidths without sacrificing sensitivity and compactness, which are important for applications in real dynamic environments.
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