  The broad line region (BLR) of luminous active galactic nuclei (AGN) is a
prominent observational signature of the accretion flow around supermassive
black holes, which can be used to measure their masses (M_BH) over cosmic
history. Due to the <100 {\mu}as angular size of the BLR, current direct
constraints on BLR kinematics are limited to those provided by reverberation
mapping studies, which are most efficiently carried out on low-luminosity L and
low-redshift z AGN. We analyze the possibility to measure the BLR size and
study its kinematic structure using spectroastrometry, whereby one measures the
spatial position centroid of emission line photons as a function of velocity.
We calculate the expected spectroastrometric signal of a rotation-dominated BLR
for various assumptions about the ratio of random to rotational motions, and
the radial distribution of the BLR gas. We show that for hyper-luminous quasars
at z < 2.5, the size of the low-ionization BLR can already be constrained with
existing telescopes and adaptive optics systems, thus providing a novel method
to spatially resolve the kinematics of the accretion flow at 10^3 -- 10^4
gravitational radii, and measure M_BH at the high-L end of the AGN family. With
a 30m-class telescope, BLR spectroastrometry should be routinely detectable for
much fainter quasars out to z ~ 6, and for various emission lines. This will
enable kinematic M_BH measurements as a function of luminosity and redshift,
providing a compelling science case for next generation telescopes.
