How allelic asymmetry is generated remains a major unsolved problem in epigenetics. Here we model the problem using X-chromosome inactivation by developing "BioRBP", an enzymatic RNA-proteomic method that enables probing of low-abundance interactions and an allelic RNA-depletion and -tagging system. We identify messenger RNA-decapping enzyme 1A (DCP1A) as a key regulator of Tsix, a noncoding RNA implicated in allelic choice through X-chromosome pairing. DCP1A controls Tsix half-life and transcription elongation. Depleting DCP1A causes accumulation of X-X pairs and perturbs the transition to monoallelic Tsix expression required for Xist upregulation. While ablating DCP1A causes hyperpairing, forcing Tsix degradation resolves pairing and enables Xist upregulation. We link pairing to allelic partitioning of CCCTC-binding factor (CTCF) and show that tethering DCP1A to one Tsix allele is sufficient to drive monoallelic Xist expression. Thus, DCP1A flips a bistable switch for the mutually exclusive determination of active and inactive Xs.