  A resistively detected NMR technique was used to probe the two-dimensional
electron gas in a GaAs/AlGaAs quantum well. The spin-lattice relaxation rate
$(1/T_{1})$ was extracted at near complete filling of the first Landau level by
electrons. The nuclear spin of $^{75}$As is found to relax much more
efficiently with $T\to 0$ and when a well developed quantum Hall state with
$R_{xx}\simeq 0$ occurs. The data show a remarkable correlation between the
nuclear spin relaxation and localization. This suggests that the magnetic
ground state near complete filling of the first Landau level may contain a
lattice of topological spin texture, i.e. a Skyrmion crystal.
