Matter-wave interferometry is ideal for detecting small forces, being able to sense changes of acceleration as small as 1 nm s^-2 as a result of quantum interference. In this thesis, I prepare a cloud of ultracold Rb-87 atoms and measure the force between an atom and a cm-sized source mass using atom interferometry. The interferometer uses a sequence of optical Raman pulses to split, reflect, and recombine the atomic wavefunction. The force that is measured is consistent with standard Newtonian gravity. Some theories that have been advanced to explain the accelerating expansion of the universe - otherwise known as dark energy - predict a departure from the Newtonian force in my experiment. I use my result to constrain the parameters of these theories. The sensitivity of the experiment is sufficient to probe physics at energies approaching the Planck scale.