The presence of the solar magnetic field has a profound effect on the structure of the lower chromosphere, and is responsible for the formation of the upper chromosphere and the corona, and the acceleration of the solar wind. The variation of the field induces variations in the chromosphere and the corona on time scales from 0.001 seconds to centries. SOHO, and subsequent approved solar missions such as TRACE will bring powerful observational capabilities to bear on critical questions relating to solar variability. However, the most fundamental question--how energy is transferred from the magnetic field into the solar plasma--will require observations of diagnostic quality on a spatial scale of 50 - 100 kilometers; this is an order of magnitude beyond the capability of any planned mission. Our mission concept, the Solar Chromospheric and Coronal Explorer (SCCE) is designed to investigate the mechanisms underlying the variability of the solar atmosphere, by attaining spectroscopic observations of the solar atmosphere over a wide range of temperatures (4,500 K to 100,000,000 K), with very high angular (0.1 arcseconds) and temporal (0.001 seconds) resolution, that will permit models of the physical processes that underlie the phenomena of solar activity to be formulated and tested at the scale, 50 - 75 kilometers that appears to be fundamental. The architecture of the SCCE is based on advances in multilayer optics, which permit broad spectral response, and high angular and spectral resolution to be achieved in a volume, and at a cost that is compatible with deployment within the fiscal and physical constraints of the MIDEX program.