We present the results of a spectroscopic survey performed in the outskirts of the globular cluster NGC1851 with VIMOS @ VLT . The radial velocities of 107 stars in a region between 12 \arcmin and 33 \arcmin around the cluster have been derived . We clearly identify the cluster stellar population over the entire field of view , indicating the presence of a significant fraction of stars outside the tidal radius predicted by King models . We also find tentative evidence of a cold ( \sigma _ { v } \leq 20 ~ { } km~ { } s ^ { -1 } ) peak in the distribution of velocities at v _ { r } \sim 180 ~ { } km~ { } s ^ { -1 } constituted mainly by Main Sequence stars whose location in the color-magnitude diagram is compatible with a stream at a similar distance of this cluster . If confirmed , this evidence would strongly support the extra-Galactic origin of this feature .