The excitation and propagation of solitary waves is studied experimentally in a two-dimensional strongly coupled dusty (complex) plasma. A single layer with ≈5000 microspheres (8μmdiam) was suspended in an argon plasma with a neutral gas pressure of 3.0mTorr. The measured Debye shielding parameter was κ≈1.6, where κ=a∕λ is the ratio of the lattice constant a to the Debye length λ. Nonlinear, planar longitudinal waves were launched by pushing all the particles in a rectangular region at the center of the crystal in the same direction using an 18W green laser. Compressive solitary waves with density perturbations δn∕n0≲0.8 and widths ≲5a were found to propagate in the forward direction at speeds exceeding the dust acoustic speed. For small amplitude solitary waves, the relations between amplitude, width, and velocity are consistent with those predicted for Korteweg–deVries solitons. Rarefactive perturbations were not observed to evolve into solitary waves. However, oscillatory shocks were seen to move in the backward direction after the laser force was removed.