The National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU) is constructing ReA3 to reaccelerate rare-isotope beams available from gas stopping of fast radio-nuclides produced by projectile fragmentation to energies of similar to 0.3-3 MeV/nucleon. Such beams are unavailable worldwide, but are in demand for Coulomb excitation and transfer reaction studies as well as for the study of astrophysical reactions. ReA3 consists of four main components: an electron-beam ion trap (EBIT), an achromatic mass separator, a radio-frequency quadrupole (RFQ) pre-accelerator, and a superconducting radio-frequency linear accelerator (SRF-LINAC). By increasing the charge of ions injected into the RFQ and SRF-LINAC, the EBIT charge breeder is a key component to provide a compact and cost-efficient reaccelerator for short-lived isotopes. The MSU EBIT will be equipped with an electron-gun cathode yielding a few amperes. A unique EBIS-EBIT hybrid magnet configuration, composed of Helmholtz coils and a solenoid, will provide a maximum magnetic field strength of 6 T. The combination of a high-current cathode and strong magnetic field will allow the MSU EBIT to reach high electron-beam current densities of 104 A/cm(2). This will make it well suited to rapidly increase the charge state of short-lived isotopes within tens of milliseconds or less. The unique extended magnet configuration will guarantee high-beam acceptance. This publication will present an overview and status of the MSU EBIT.