  We study the effect that quantum fluctuations produced during the nucleation
of a single-bubble open inflationary universe have on the amplitude of
temperature anisotropies in the microwave background. We compute the instanton
action for the quantum tunneling between the false and true vacua in open
inflation models and show that the amplitude of quantum fluctuations of the
bubble wall is very sensitive to the gravitational effects of the true vacuum.
We study the spectrum of quantum fluctuations of the bubble wall and confirm
that there is only an inhomogeneous ($k^2 = -3$) discrete mode associated with
transverse traceless fluctuations of the bubble wall. This super-curvature mode
could in principle distort the anisotropy of the microwave background. We
compute the amplitude of the gauge invariant metric perturbations induced by
the bubble wall fluctuations on a comoving hypersurface, and calculate the
induced amplitude of temperature fluctuations in the microwave background, for
arbitrary values of $\Omega_0$. We find that in the limit $\Omega_0\simeq 1$,
the quadrupole dominates the angular power spectrum, like in the usual
Grishchuk-Zel'dovich effect. The resulting bounds on the amplitude of quantum
fluctuations of the bubble wall from the absence of such an effect in the
observed microwave background anisotropies are quite strong. We also study the
contribution from a discrete long wavelength super-curvature mode ($k^2 \simeq
2m^2/3H^2$) that appears in the spectrum of open de Sitter vacuum fluctuations.
We constrain the parameters of the models of open inflation so that these modes
do not distort the observed temperature anisotropy.
