The regulatory specificity of enhancers and their interaction with gene promoters is thought to be controlled by their sequence and the binding of transcription factors. By studying Pitx1, a regulator of hindlimb development, we show that dynamic changes in chromatin conformation can restrict the activity of enhancers. Inconsistent with its hindlimb-restricted expression, Pitx1 is controlled by an enhancer (Pen) that shows activity in forelimbs and hindlimbs. By Capture Hi-C and three-dimensional modeling of the locus, we demonstrate that forelimbs and hindlimbs have fundamentally different chromatin configurations, whereby Pen and Pitx1 interact in hindlimbs and are physically separated in forelimbs. Structural variants can convert the inactive into the active conformation, thereby inducing Pitx1 misexpression in forelimbs, causing partial arm-to-leg transformation in mice and humans. Thus, tissue-specific three-dimensional chromatin conformation can contribute to enhancer activity and specificity in vivo and its disturbance can result in gene misexpression and disease.