  In this paper we construct an abelian fibration over ${\bf P}^3$ on the
Hilbert cube of the primitive K3 surface of genus 9. After the abelian
fibration constructed by Mukai on the Hilbert square on the primitive K3
surface S of genus 5, this is the second example where the abelian fibration on
such Hilb_n(S) is directly constructed. Our example is also the first known
abelian fibration on a Hilbert scheme Hilb_n(S) of a primitive K3 surface S
which is not the Hilbert square of S; the primitive K3 surfaces on the Hilbert
square of which such a fibration exists are known by a recent result of Hassett
and Tschinkel.
