  A low energy radioactive beam of polarized $^8$Li has been used to observe
the vortex lattice near the surface of superconducting NbSe$_2$. The
inhomogeneous magnetic field distribution associated with the vortex lattice
was measured using depth-resolved $\beta$-detected NMR. Below $T_c$ one
observes the characteristic lineshape for a triangular vortex lattice which
depends on the magnetic penetration depth and vortex core radius. The size of
the vortex core varies strongly with magnetic field. In particular in a low
field of 10.8 mT the core radius is much larger than the coherence length. The
possible origin of these giant vortices is discussed.
