Small-angle neutron scattering has been employed to study the influence of applied electric (E-)fields on the skyrmion lattice in the chiral lattice magnetoelectric Cu₂OSeO₃. Using an experimental geometry with the E-field parallel to the [111] axis, and the magnetic field parallel to the [11̄0] axis, we demonstrate that the effect of applying an E-field is to controllably rotate the skyrmion lattice around the magnetic field axis. Our results are an important first demonstration for a microscopic coupling between applied E-fields and the skyrmions in an insulator, and show that the general emergent properties of skyrmions may be tailored according to the properties of the host system.