We report the first extrasolar planet observations from the 10.4-m Gran Telescopio Canarias (GTC), currently the world's largest, fully steerable, single-aperture optical telescope. We used the OSIRIS tunable filter imager on the GTC to acquire high-precision, narrow-band photometry of the transits of the giant exoplanets, TrES-2b and TrES-3b. We obtained near-simultaneous observations in two near-infrared (NIR) wavebands (790.2 and 794.4 +/- 2.0 nm) specifically chosen to avoid water vapor absorption and skyglow so as to minimize the atmospheric effects that often limit the precision of ground-based photometry. Our results demonstrate a very-high photometric precision with minimal atmospheric contamination despite relatively poor atmospheric conditions and some technical problems with the telescope. We find the photometric precision for the TrES-2 observations to be 0.343 and 0.412 mmag for the 790.2 and 794.4 nm light curves, and the precision of the TrES-3 observations was found to be 0.470 and 0.424 mmag for the 790.2 and 794.4 nm light curves. We also discuss how future follow-up observations of transiting planets with this novel technique can contribute to the characterization of Neptune- and super-Earth-size planets to be discovered by space-based missions like CoRoT and Kepler, as well as measure atmospheric properties of giant planets, such as the strength of atmospheric absorption features.

9 pages, including 3 figures and 2 tables; accepted for publication in MNRAS