In recent years, many new camera designs have been proposed which preserve image detail over a larger depth range than conventional cameras. These methods rely on either mechanical motion or a custom optical element placed in the pupil plane of a camera lens to create the desired point spread function (PSF). This work introduces a new Spectral Focal Sweep (SFS) camera which can be used to extend depth of field (DOF) when some information about the reflectance spectra of objects being imaged is known. Our core idea is to exploit the principle that for a lens without chromatic correction, the focal length varies with wavelength. We use a SFS camera to capture an image that effectively "sweeps" the focal plane continuously through a scene without the need for either mechanical motion or custom optical elements. We demonstrate that this approach simplifies lens design constraints, enabling an inexpensive implementation to be constructed with off-the-shelf components. We verify the effectiveness of our implementation and show several example images illustrating a significant increase in DOF over conventional cameras.