An optical coherence microscopy system based on line illumination and detection is demonstrated. The system uses a Linnik-type interferometer illuminated by a broadband Ti:sapphire laser and detected by a high-speed, line-scan CCD camera. This approach is less sensitive to incoherent scattering and sample motion than full-field imaging. Spatial resolutions of $\sim 2\mu \mathrm{m}\times \sim 3\mu \mathrm{m}$ $(\text{transverse}\times \text{axial})$ are achieved. The sensitivity of the system is $93\mathrm{dB}$ with averaging over 30 line scans. En face real time, cellular-level imaging of biological tissues is demonstrated at $\sim 2\text{\hspace{0.17em} frames}∕\mathrm{s}$ .