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We present N-body simulations of resonant planets with inclined orbits thatshow chaotically evolving eccentricities and inclinations that can persist forat least 10 Gyr. A wide range of behavior is possible, from fast, low amplitudevariations to systems in which eccentricities reach 0.9999 and inclinations179.9 degrees. While the orbital elements evolve chaotically, at least oneresonant argument always librates. We show that the HD 73526, HD 45364 and HD60532 systems may be in chaotically-evolving resonances. Chaotic evolution isapparent in the 2:1, 3:1 and 3:2 resonances, and for planetary masses fromlunar- to Jupiter-mass. In some cases, orbital disruption occurs after severalGyr, implying the mechanism is not rigorously stable, just long-lived relativeto the main sequence lifetimes of solar-type stars. Planet-planet scatteringappears to yield planets in inclined resonances that evolve chaotically inabout 0.5% of cases. These results suggest that 1) approximate methods foridentifying unstable orbital architectures may have limited applicability, 2)the observed close-in exoplanets may be produced during the high eccentricityphases induced by inclined resonances, 3) those exoplanets' orbital planes maybe misaligned with the host star's spin axis, 4) systems with resonances may besystematically younger than those without, 5) the distribution of period ratiosof adjacent planets detected via transit may be skewed due to inclinedresonances, and 6) potentially habitable planets in resonances may havedramatically different climatic evolution than the Earth. The GAIA spacecraftis capable of discovering giant planets in these types of orbits.

Long-lived Chaotic Orbital Evolution of Exoplanets in Mean Motion Resonances with Mutual Inclinations