We have developed a new, high performance, hyperspectral microscope for biological and other applications. For each voxel within a three-dimensional specimen, the microscope simultaneously records the emission spectrum from 500\text{\hspace{0.17em} nm} to \text{800 \hspace{0.17em} nm} , with better than \text{3 \hspace{0.17em} nm} spectral resolution. The microscope features a fully confocal design to ensure high spatial resolution and high quality optical sectioning. Optical throughput and detection efficiency are maximized through the use of a custom prism spectrometer and a backside thinned electron multiplying charge coupled device (EMCCD) array. A custom readout mode and synchronization scheme enable 512-point spectra to be recorded at a rate of 8300 spectra per second. In addition, the EMCCD readout mode eliminates curvature and keystone artifacts that often plague spectral imaging systems. The architecture of the new microscope is described in detail, and hyperspectral images from several specimens are presented.