We report on the occurrence of sharp Fano resonances in planar terahertz metamaterials by introducing a weak asymmetry in a two gap split ring resonator. As the structural symmetry of the metamaterial is broken a Fano resonance evolves in the low-frequency flank of the symmetric fundamental dipole mode resonance. This Fano resonance can have much higher Q factors than that known from single gap split ring resonators. Supporting simulations indicate a Q factor of 50 for lowest degree of asymmetry. The Q factor decreases exponentially with increasing asymmetry. Hence, minute structural variations allow for a tuning of the Fano resonance. Such sharp resonances could be exploited for biochemical sensing. Besides, the strong current oscillations excited at the Fano resonance frequency could lead to the design of novel terahertz narrow band emitters.