Individual quantum dots are often referred to as "artificial atoms." Two tunnel-coupled quantum dots can be considered an "artificial molecule." Low-temperature measurements were made on a series double quantum dot with adjustable interdot tunnel conductance that was fabricated in a gallium arsenide-aluminum gallium arsenide heterostructure, The Coulomb blockade was used to determine the ground-state charge configuration within the "molecule" as a function of the total charge on the double dot and the interdot polarization induced by electrostatic gates. As the tunnel conductance between the two dots is increased from near zero to 2e (2)/h (where e is the electron charge and h is Planck’s constant), the measured conductance peaks of the double dot exhibit pronounced changes in agreement with many-body theory.