  In common with other iron-based high temperature superconductors, FeSe
exhibits a transition to a ``nematic'' phase below 90Kelvin in which the
crystal rotation symmetry is spontaneously broken. However, the absence of
strong low-frequency magnetic fluctuations near or above the transition has
been interpreted as implying the primacy of orbital ordering. In contrast, we
establish that quantum fluctuations of spin-1 local moments with strongly
frustrated exchange interactions can lead to a nematic quantum paramagnetic
phase consistent with the observations in FeSe. We show that this phase is a
fundamental expression of the existence of a Berry's phase associated with the
topological defects of a N\'eel antiferromagnet, in a manner analogous to that
which gives rise to valence bond crystal order for spin 1/2 systems. We present
an exactly solvable model realizing the nematic quantum paramagnetic phase,
discuss its relation with the spin-1 $J_1-J_2$ model, and construct a field
theory of the Landau-forbidden transition between the N\'eel state and this
nematic quantum paramagnet.
