  We have observed the cold collision frequency shift of the 1S-2S transition
in trapped spin-polarized atomic hydrogen. We find $\Delta \nu_{1S-2S} =
-3.8(8)\times 10^{-10} n Hz cm^3$, where $n$ is the sample density. From this
we derive the 1S-2S s-wave triplet scattering length, $a_{1S-2S}=-1.4(3)$ nm,
which is in fair agreement with a recent calculation. The shift provides a
valuable probe of the distribution of densities in a trapped sample.
