We report results from molecular dynamics simulations of water under confinement and at ambient conditions that predict a first-order freezing transition from a monolayer of liquid water to a monolayer of ice induced by increasing the distance between the confining parallel plates. Since a slab geometry is incompatible with a tetrahedral arrangement of the sp(3) hybridized oxygen of water, the freezing is coupled to a linear buckling transition. By exploiting the ordered out-of-plane displacement of the molecules in the buckled phase the distortion of the hydrogen bonds is minimized.