We have built a high-resolution optical coherence tomography (OCT) system, based on a Linnik-type interference microscope, illuminated by a white-light thermal lamp. The extremely short coherence length of the illumination source and the large aperture of the objectives permit resolution close to 1 mm in three dimensions. A parallel detection scheme with a CCD camera provides cross-section x y image acquisition without scanning at a rate of up to 50 Hz. To our knowledge, our system has the highest resolution demonstrated to date for OCT imaging. With identical resolution in three dimensions, realistic volume rendering of structures inside biological tissues is possible.