The coherent generation of synchrotron radiation by an electron storage ring is predicted for wavelengths equal to or longer than the electron bunch length. With typical bunch lengths of approximately 1 cm, diffraction and chamber-screening effects have so far blocked observation of coherent radiation from a conventional radiation beamline. In the low-energy, second-generation light source MAX-I, the magnet lattice has been tuned to a small momentum compaction factor, allowing rms bunch lengths as short as 1 mm. Here we report the coherent far-infrared emission observed from such a bunch. The paper discusses the origin of coherent synchrotron radiation for Gaussian and non-Gaussian electron bunches, and the procedure used to generate such bunches. The emission was characterized using the infrared beamline at MAX-I, including an interferometer, a liquid-helium-cooled bolometer detector, waveguide high-pass filters, and a conductive-grid polarization filter. The intensity of the coherent radiation is greater by a factor of 2x103 to 6x103 than normal incoherent synchrotron radiation, and is seen between 8 and 22 cm-1.