In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedmann-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wave-length). For ( 1 − Ω ) ≪ 1 , where Ω is the density parameter, the microwave temperature anisotropies produced by these modes are of order δ T T ∼ H ( R 0 μ l ) − 1 2 ( 1 − Ω ) l 2 . Here, H is the expansion rate during inflation, R 0 is the intrinsic radius of the bubble at the time of nucleation, μ is the bubble wall tension, and l labels the different multipoles ( l > 1 ). The gravitational back reaction of the bubble has been ignored. In this approximation, G μ R 0 ≪ 1 , and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course, Ω gets too close to 1, in which case the new effect disappears).