We study Vassiliev invariants of Brunnian links, which are links
 whose proper sublinks are all trivial.
 It is known that a Brunnian link with (n+1)>2 components cannot be
 distinguished from the unlink by any Vassiliev invariant of degree
 <2n.
 The purpose of this talk is to study the first nontrivial case. We
 will show that the restriction of an invariant of degree 2n to
 (n+1)-component Brunnian links can be expressed as a quadratic form
 on the Milnor link-homotopy invariants of length n+1.