  Let $\gamma_n$ be the standard Gaussian measure on $\mathbb{R}^n$. We prove
that for every symmetric convex sets $K,L$ in $\mathbb{R}^n$ and every
$\lambda\in(0,1)$, $$\gamma_n(\lambda K+(1-\lambda)L)^{\frac{1}{n}} \geq
\lambda \gamma_n(K)^{\frac{1}{n}}+(1-\lambda)\gamma_n(L)^{\frac{1}{n}},$$ thus
settling a problem raised by Gardner and Zvavitch (2010). This is the Gaussian
analogue of the classical Brunn-Minkowski inequality for the Lebesgue measure.
We also show that, for a fixed $\lambda\in(0,1)$, equality is attained if and
only if $K=L$.
