Colossal magnetoresistance—a huge decrease in resistance in response to a magnetic field—has recently been observed in manganese oxides with perovskite structure. This effect is attracting considerable interest from both fundamental and practical points of view1. In the context of using this effect in practical devices, a noteworthy feature of these materials is the high degree of spin polarization of the charge carriers, caused by the half-metallic nature of these materials20,21; this in principle allows spin-dependent carrier scattering processes, and hence the resistance, to be strongly influenced by low magnetic fields. This type of field control has been demonstrated for charge-carrier scattering at tunnelling junctions2,3 and at crystal-twin or ceramic grain boundaries4,5, although the operating temperature of such structures is still too low (⩽150 K) for most applications. Here we report a material—Sr2FeMoO6, an ordered double perovskite6—exhibiting intrinsic tunnelling-type magnetoresistance at room temperature. We explain the origin of this behaviour with electronic-structure calculations that indicate the material to be half-metallic. Our results show promise for the development of ordered perovskite magnetoresistive devices that are operable at room temperature.