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We study the observable implications of an incomplete first order phase transition during inflation. In such a phase transition, the nucleated bubbles do not percolate and instead are continuously produced until the onset of reheating. The process creates an inhomogeneity with a distinct power spectrum that depends on both the physics of the phase transition and the inflationary dynamics. Upon horizon re-entry, this spectrum generates gravitational waves through non-linear effects. This stochastic gravitational wave background is predicted to have unique signatures that may be detectable by future experiments spanning a wide frequency range. The discovery of such a gravitational wave signal would shed a light on the detailed dynamics of inflation.