We present systematic measurements of the surface rheology of monolayers of liquid-condensed (LC) dipalmitoylphosphatidylcholine (DPPC) at the air-water interface. Using microfabricated, ferromagnetic 'microbuttons' as new microrheological probes, we measure the linear viscoelastic moduli of LC DPPC monolayers as both surface pressure and frequency are varied. Visualization of this interface reveals that the interlocked liquid crystalline domains that comprise an LC-DPPC monolayer give rise to a viscoelastic solid response. Two distinct behaviors arise as surface pressure is increased: for low surface pressures (8 mN m-1 ≤ Π ≤ 12-14 mN m-1), the monolayer behaves like a two-dimensional emulsion, with a surface elastic modulus G′s that is relatively constant, as would be expected from a line tension-mediated elasticity. The surface viscosity increases exponentially with Π, as would be expected for a condensed liquid monolayer. Above 12-14 mN m-1, however, both moduli increase exponentially with Π, albeit with a weaker slope - a response that would not be expected from line-tension-mediated elasticity. This transition would be consistent with a second-order phase transition between the LC and solid-condensed phase, as has been observed in other phospholipid monolayers. Finally, we employ a controlled-stress (creep) mode to find a stress-dependent viscosity bifurcation, and thus the yield stress of this monolayer.