Systems with a ferroelectric to paraelectric transition in the vicinity of room temperature are useful for devices. Adjusting the ferroelectric transition temperature (T-c) is traditionally accomplished by chemical substitution - as in BaxSr1-xTiO3, the material widely investigated for microwave devices in which the dielectric constant (epsilon(r)) at GHz frequencies is tuned by applying a quasi-static electric field(1,2). Heterogeneity associated with chemical substitution in such films, however, can broaden this phase transition by hundreds of degrees(3), which is detrimental to tunability and microwave device performance. An alternative way to adjust Tc in ferroelectric films is strain(4-8). Here we show that epitaxial strain from a newly developed substrate can be harnessed to increase Tc by hundreds of degrees and produce room-temperature ferroelectricity in strontium titanate, a material that is not normally ferroelectric at any temperature. This strain-induced enhancement in T-c is the largest ever reported. Spatially resolved images of the local polarization state reveal a uniformity that far exceeds films tailored by chemical substitution. The high er at room temperature in these films ( nearly 7,000 at 10 GHz) and its sharp dependence on electric field are promising for device applications(1,2).