I will describe measurements of individual phonons in a 1 ng body of superfluid helium. When this body is in equilibrium, the phonon correlations are those of a thermal state with mean occupancy ~ 1. The purity of the state is preserved even when the mode is driven to a coherent state whose amplitude corresponds to ~100,000 phonons. I will describe how these results constrain a certain class of nonlinear extensions of quantum mechanics. We find that our data places constraints at roughly the same level as experiments at the Large Hadron Collider.