Most existing electron sources extract electrons from conductors. Since the actual temperature inside the conductor is much less than the Fermi temperature of the conduction electrons, the electron degeneracy (delta_f) is close to 1, the maximum allowed by the Pauli exclusion principle. However, during extraction several factors conspire together to reduce delta_f many orders of magnitude, limiting the achieved values to approx 10-5. A new concept is described for building a novel electron source designed to produce a pulsed beam with delta_f approx 2~;10-3 and longitudinal emittance four orders of magnitude smaller than currently achieved values. This high brightness, low longitudinal emittance regime enables a wide range of novel applications that utilize angstrom-scale spatial resolution and eV-scale energy resolution. The current state of a proof-of-principle experiment conducted at LBNL is also described.