  We present ab initio lattice calculations of the low-energy even-parity
states of $^{16}$O using chiral nuclear effective field theory. We find good
agreement with the empirical energy spectrum, and with the electromagnetic
properties and transition rates. For the ground state, we find that the
nucleons are arranged in a tetrahedral configuration of alpha clusters. For the
first excited spin-0 state, we find that the predominant structure is a square
configuration of alpha clusters, with rotational excitations that include the
first spin-2 state.
