The stretching of single, tethered DNA molecules by a flow was directly visualized with fluorescence microscopy. Molecules ranging in length (L) from 22 to 84 micrometers were held stationary against the flow by the optical trapping of a latex microsphere attached to one end. The fractional extension x/L is a universal function of eta vL(0.54+/-0.05), where eta and v are the viscosity and velocity of the flow, respectively. This relation shows that the DNA is not "free-draining" (that is, hydrodynamic coupling within the chain is not negligible) even near full extension (similar to 80 percent). This function has the same form over a lone range as the fractional extension versus force applied at the ends of a worm-like chain. For small deformations (<30 percent of full extension), the extension increases with velocity as x similar to v(0.70+/-0.08). The relative size of fluctuations in extension decreases as sigma(x)/x congruent to 0.42 exp(-4.9 x/L). Video images of the fluctuating chain have a cone-like envelope and show as sharp increase in intensity at the free end.