  We quantify the distribution of [OIII]+H$\beta$ line strengths at z$\simeq$7
using a sample of 20 bright (M$_{\mathrm{UV}}$ $\lesssim$ $-$21) galaxies. We
select these systems over wide-area fields (2.3 deg$^2$ total) using a new
colour-selection which precisely selects galaxies at z$\simeq$6.63$-$6.83, a
redshift range where blue Spitzer/IRAC [3.6]$-$[4.5] colours unambiguously
indicate strong [OIII]$+$H$\beta$ emission. These 20 galaxies suggest a
log-normal [OIII]$+$H$\beta$ EW distribution with median EW =
759$^{+112}_{-113}$ $\mathrm{\mathring{A}}$ and standard deviation =
0.26$^{+0.06}_{-0.05}$ dex. We find no evidence for strong variation in this EW
distribution with UV luminosity. The typical [OIII]+H$\beta$ EW at z$\simeq$7
implied by our sample is considerably larger than that in massive star forming
galaxies at z$\simeq$2, consistent with a shift toward larger average sSFR (4.4
Gyr$^{-1}$) and lower metallicities (0.16 Z$_\odot$). We also find evidence for
the emergence of a population with yet more extreme nebular emission
([OIII]+H$\beta$ EW$>$1200 $\mathrm{\mathring{A}}$) that is rarely seen at
lower redshifts. These objects have extremely large sSFR ($>$30 Gyr$^{-1}$), as
would be expected for systems undergoing a burst or upturn in star formation.
While this may be a short-lived phase, our results suggest that 20% of the
z$\simeq$7 population has such extreme nebular emission, implying that galaxies
likely undergo intense star formation episodes regularly at z$>$6. We argue
that this population may be among the most effective ionizing agents in the
reionization era, both in terms of photon production efficiency and escape
fraction. We furthermore suggest that galaxies passing through this large sSFR
phase are likely to be very efficient in forming bound star clusters.
