A new instrument for measuring magnetic fields in the sun's atmosphere has recently been installed at the National Solar Observatory in New Mexico. At each point within the field of view, it detects both linear and circular polarization in a spectral line from which the solar magnetic field strength and direction may be deduced. The vector magnetograph has low instrumental polarization and low circular-to-linear crosstalk. Spectral resolution is provided by a solid lithium-niobate Fabry-Perot filter which may be electrically tuned to scan any solar spectral line. The instrument is capable of 0.7 arc second spatial resolution and 0.015 nm spectral resolution. Prior to installation, tests were conducted at the Applied Physics Laboratory to evaluate the polarimeter components. The instrument and its background are described, together with some test results.