Down's syndrome is a common disorder with enormous medical and social costs, caused by trisomy for chromosome 21. We tested the concept that gene imbalance across an extra chromosome can be de facto corrected by manipulating a single gene, XIST (the X-inactivation gene). Using genome editing with zinc finger nucleases, we inserted a large, inducible XIST transgene into the DYRK1A locus on chromosome 21, in Down's syndrome pluripotent stem cells. The XIST non-coding RNA coats chromosome 21 and triggers stable heterochromatin modifications, chromosome-wide transcriptional silencing and DNA methylation to form a 'chromosome 21 Barr body'. This provides a model to study human chromosome inactivation and creates a system to investigate genomic expression changes and cellular pathologies of trisomy 21, free from genetic and epigenetic noise. Notably, deficits in proliferation and neural rosette formation are rapidly reversed upon silencing one chromosome 21. Successful trisomy silencing in vitro also surmounts the major first step towards potential development of 'chromosome therapy'.