The first observation of the decay $\kstarkstar$ is reported using 35\invpb of data collected by LHCb in proton-proton collisions at a centre-of-mass energy of 7 TeV. A total of $49.8 \pm 7.5$ $B^0_s \rightarrow (K^+\pi^-)(K^-\pi^+)$ events are {observed within $\pm 50 \mevcc$ of the \Bs mass and $746 \mevcc < m_{K\pi}< 1046 \mevcc$, mostly coming from a resonant $\kstarkstar$ signal.} The branching fraction and the \CP-averaged \Kstarz longitudinal polarization fraction are measured to be {$\BR(\kstarkstar) = (2.81 \pm 0.46 ({\rm stat.}) \pm 0.45 ({\rm syst.}) \pm 0.34\, (f_s/f_d))\times10^{-5}$} and $f_L = 0.31 \pm 0.12 ({\rm stat.}) \pm 0.04 ({\rm syst.})$.