  The non-Gaussianity of initial perturbations provides information on the
mechanism that generated primordial density fluctuations. The expected
non-Gaussianity for slow-roll inflationary models is well below the ultimate
detection level with cosmic microwave background (CMB) anisotropies or
large-large structure at low redshifts. We find that 21-cm background
anisotropies of the low-frequency radio sky due to inhomogeneous neutral
Hydrogen distribution at redshifts between 30 and 100 captures information on
primordial non-Gaussianity better than any other cosmological probe. An all-sky
21-cm experiment over the frequency range from 14 MHz to 40 MHz using a
bandwidth of 1 MHz and with angular information out to a multipole of 10^5 can
limit the primordial non-Gaussianity parameter f_nl < 0.01. The 21-cm
background should eventually reveal the non-Gaussianity associated with single
field slow-roll inflation.
