F-regularity does not deform

We show that the property of F-regularity does not deform, and thereby settle a longstanding open question in the theory of tight closure. Specifically, we construct a three dimensional N-graded domain R which is not F-regular (or even F-pure), but has a quotient R / tR which is F-regular. Examples are constructed over fields of characteristic p > 0, as well as over fields of characteristic zero.