We consider a gas of bosons interacting through a hard-sphere potential with radius \frak{a} in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the leading term 4\pi \frak{a} \rho and shows that corrections are of order smaller than \rho \frak{a} (\rho \frak{a}^3)^{1/2-\epsilon}, for any \epsilon > 0.
