0 + 0 > 0

In this Letter we show that quantum nonlocality can be superactivated.That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself.In the second part of this work we study how large these violations can be.In particular, we show the existence of quantum states with very low Bell violation but such that five copies of them give very large violations.In fact, this gap can be made arbitrarily large by increasing the dimension of the states.