We utilize synthetic-aperture Fourier holographic microscopy to resolve micrometer-scale microstructure over millimeter-scale fields of view. Multiple holograms are recorded, each registering a different, limited region of the sample object's Fourier spectrum. They are "stitched together" to generate the synthetic aperture. A low-numerical-aperture (NA) objective lens provides the wide field of view, and the additional advantages of a long working distance, no immersion fluids, and an inexpensive, simple optical system. Following the first theoretical treatment of the technique, we present images of a microchip target derived from an annular synthetic aperture (NA = 0.61) whose area is 15 times that due to a single hologram (NA = 0.13); they exhibit a corresponding qualitative improvement. We demonstrate that a high-quality reconstruction may be obtained from a limited sub-region of Fourier space, if the object's structural information is concentrated there.