NASA’s Space Interferometry Mission (SIM), scheduled for launch in 2009, will determine the positions of thousands of stars as faint as V = 20 to a precision better than 4 microarcseconds (µas). A key part of the mission is the Astrometric Grid, which is a reference frame of several thousand stars with V ≤ 13 against which all relative measurements will be calibrated. To serve as a reliable inertial reference frame, the Grid must be astrometrically stable against photocenter jitter (from planets, binary companions, flaring or spotting) at the ~ 4µas level. Sub–solar metallicity giant stars, by virtue of their intrinsic luminosity, can probe the Galaxy to greater distances than almost any other stellar type at the same apparent magnitude. Thus, distant (> 3 kpc) giants with V < 13 will have proportionately smaller astrometric jitter compared to other potential Astrometric Grid star candidates. The Grid Giant Star Survey is a patchwork all-sky survey to find sub–solar metallicity K giants for the Grid, and to provide a unique database for studies of Galactic stellar populations. We describe here the survey characteristics and give examples of results to date.