Rates of hiring and job separation fell by as much as a third in the U.S. between the late 1990s and the early 2010s. Half of this decline is associated with the declining incidence of jobs that start and end in the same calendar quarter, employment events that we call "single quarter jobs." We investigate this unique subset of jobs and its decline using matched employer-employee data for the years 1996-2012. We characterize the worker demographics and employer characteristics of single quarter jobs, and demonstrate that changes over time in workforce and employer composition explain little of the decline in these jobs. We find that the decline in these jobs accounts for about a third of the decline in the fraction of the population that holds a job in the private sector that occurred from the mid -2000s to the early 2010s. We also find little evidence that single quarter jobs are stepping stones into longer-term employment. Finally, we show that the inclusion or exclusion of these single quarter jobs creates divergent trends in average earnings and the dispersion of earnings for the years 1996-2012. To the extent that administrative records measure the volatile tail of the employment distribution better than conventional household surveys, these findings show that measurement of short duration jobs matters for economic analysis.