This project will measure the spin projection of cold atoms with unprecedented precision, and apply this measurement to create an ultraprecise microscope for magnetic fields. Using a spinor Bose-Einstein condensate as a magnetic field sensor, we will measure the precession of the condensate spin with exquisite sensitivity. This will be the first direction measurement of a macroscopic quantum spin to break the standard quantum limit and show that the uncertainty principle need not limit such spin measurements. The spinor magnetometer will be one million times more sensitive than conventional magnetometers of the same size and will detect the miniscule magnetic fields of biological cells and microstructured superconducting films.