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Novel devices only offer reasonable telecommunication solutions when they can be packaged and manufactured efficiently and at low cost. We demonstrate such a compact and power efficient tunable dispersion compensating fiber Bragg grating (FBG) device. The device relies on a distributed on-fiber thin-film heater deposited onto the outer surface of an unchirped FBG. Current flowing though the thin film generates resistive heating that is governed by the thickness profile of the metal film. A chirp in the grating is obtained by using a coating whose thickness varies with position along the length of the grating in a prescribed manner; the chirp rate is adjusted by varying the applied current. Using an electrical power of less than 1 W in a packaged device, we demonstrate a linearly chirped Bragg grating in which the dispersion is continuously tuned from -300 to -1350 ps/nm, with an average deviation from linearity of approximately 10 ps.