  Cosmological measurements of the 21-cm line of neutral hydrogen are poised to
dramatically enhance our understanding of the early universe. In particular,
both the epochs of reionization and cosmic dawn remain largely uncharted, and
the 21-cm signal is one of the few probes to reach them. The simplest 21-cm
measurement is the global signal (GS), which corresponds to the averaged
absorption or emission of 21-cm photons across the entire sky. While bright
radio foregrounds swamp the cosmic signal over the entire frequency range
observable, presenting a formidable hurdle, they can in principle be
subtracted, given enough sensitivity. Here, however, we point out an
additional---and irreducible---source of uncertainty for the 21-cm GS: cosmic
variance. The cosmic-variance noise arises from the finite volume of the
universe accessible to 21-cm experiments. Due to the cosmological redshifting
of 21-cm photons, each observed frequency probes our universe during a
particular cosmic age, corresponding to a narrow redshift slice. The presence
of large 21-cm fluctuations makes the GS within each slice different than the
GS averaged over the entire universe. We estimate the size of this
cosmic-variance noise, and find that for a standard scenario it has a size of
$\sim 0.1$ mK, which is $\sim 10\%$ of the size of the expected instrumental
noise of a year-long experiment. Interestingly, cosmic variance can overtake
instrumental noise for scenarios with extreme 21-cm fluctuations, such as those
suggested to explain the sharpness of the claimed EDGES detection. Moreover, as
large-scale 21-cm fluctuations are coherent over long distances, cosmic
variance correlates the measurements of the GS at nearby redshifts, leading to
off-diagonal uncertainties that have so far been neglected.
