The superheating of a solid to a temperature beyond its melting point, without the solid actually melting, is a well-known phenomenon. It occurs with many substances, particularly those that can readily be produced as high-quality crystals. In principle, ice should also be amenable to superheating. But the complex three-dimensional network of hydrogen bonds that holds water molecules together and gives rise to unusual solid and liquid properties strongly affects the melting behaviour of ice; in particular, ice usually contains many defects owing to the directionality of its hydrogen bonds. However, simulations are readily able to `create' defect-free ice that can be superheated. Here we show that by exciting the OH stretching mode of water, it is possible to superheat ice. When using an ice sample at an initial temperature of 270K, we observe an average temperature rise of 20 +/- 2K that persists over the monitored time interval of 250ps without melting.