We consider the height H(x, t) of the PNG droplet for large time t.  The typical fluctuations for h are of the order t^{1/3}.  The transverse correlations are on the scale x = y t^{2/3}, y of order 1.  We establish that the limit process is the Airy process A(y).  A(y) is stationary with single-point distribution as Tracy-Widom.  The Airy process is the lst line in Dyson's Brownian motion under edge scaling.