Genome sequencing has uncovered a new mutational phenomenon in cancer and congenital disorders called chromothripsis. Chromothripsis is characterized by extensive genomic rearrangements and an oscillating pattern of DNA copy number levels, all curiously restricted to one or a few chromosomes. The mechanism for chromothripsis is unknown, but we previously proposed that it could occur through the physical isolation of chromosomes in aberrant nuclear structures called micronuclei. Here, using a combination of live cell imaging and single-cell genome sequencing, we demonstrate that micronucleus formation can indeed generate a spectrum of genomic rearrangements, some of which recapitulate all known features of chromothripsis. These events are restricted to the mis-segregated chromosome and occur within one cell division. We demonstrate that the mechanism for chromothripsis can involve the fragmentation and subsequent reassembly of a single chromatid from a micronucleus. Collectively, these experiments establish a new mutational process of which chromothripsis is one extreme outcome. The mechanism for chromothripsis, “shattered” chromosomes that can be observed in cancer cells, is unknown; here, using live-cell imaging and single-cell sequencing, chromothripsis is shown to occur after a chromosome is isolated into a micronucleus, an abnormal nuclear structure. Chromothripsis, a dramatic chromosomal event involving massive chromosome breakage and rearrangement, typically restricted to one or a few of a cell's chromosomes, has been observed in various cancers and congenital diseases. A new study uses a combination of live-cell imaging and single-cell genome sequencing to recreate chromothripsis-like rearrangements. The results show that after single chromosomes are missegregated into so-called micronuclei, they can shatter. After cell division, these fragments can be incorporated back into the genome, generating rearrangements that in some cases bear all the hallmark features of chromothripsis. Chromosome shattering in micronuclei can also lead to the formation of small circular chromosome fragments, the initial step in forming 'double minute chromosomes', which carry amplified oncogenes in cancer. This study thus provides the first experimental demonstration of a molecular mechanism underlying chromothripsis.