We use Atacama Large Millimeter/submillimeter Array CO (2–1) observations of six low-redshift Palomar-Green quasars to study the distribution and kinematics of the molecular gas of their host galaxies at kiloparsec-scale resolution. While the molecular gas content, molecular gas fraction, and star formation rates are similar to those of nearby massive, star-forming galaxies, the quasar host galaxies possess exceptionally compact, disky molecular gas distributions with a median half-light radius of 1.8 kpc and molecular gas mass surface densities ≳22 M
⊙ pc−2. While the overall velocity field of the molecular gas is dominated by regular rotation out to large radii, with ratio of rotation velocity to velocity dispersion ≳9, the nuclear region displays substantial kinematic complexity associated with small-scale substructure in the gas distribution. A tilted-ring analysis reveals that the kinematic and photometric position angles are misaligned on average by ∼ 34° ± 26° and provides evidence of kinematic twisting. These observations provide tantalizing clues to the detailed physical conditions of the circumnuclear environments of actively accreting supermassive black holes.