  We consider the (de)focusing cubic Gross-Pitaevskii (GP) hierarchy on
$\mathbb{R}$, which is an infinite hierarchy of coupled linear inhomogeneous
PDE which appears in the derivation of the cubic nonlinear Schr\"{o}dinger
(NLS) equation from quantum many-particle systems. Motivated by the fact that
the cubic NLS on $\mathbb{R}$ is an integrable equation which admits infinitely
many conserved quantities, we exhibit an infinite sequence of operators which
generate analogous conserved quantities for the GP hierarchy.
