It is shown that superstring (and heterotic string) theory has negative energy solutions that asymptotically resemble toroidal compactifications with constant gauge fields. The toroidal compactifications are not supersymmetric but are tachyon free. This implies that the corresponding flat, zero energy toroidal compactifications are unstable. Instantons are presented that describe semiclassical tunnelling from these flat vacua to nonflat zero energy solutions.