We present ∼1" resolution 1.3 millimeter dust continuum and spectral line (12CO and 13CO J=2-1) observations of the transitional disk system HD 135344B obtained with the Submillimeter Array. The disk shows a Keplerian rotation pattern with an inclination of ∼11, based on the spatially and spectrally resolved 12CO and 13CO emission. The data show clear evidence for both dust and gas surface density reductions in the inner region of the disk (radius ≲ 50 AU) from the continuum and 13CO J=2-1

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... respectively. The presence of this inner cavity in both the dust and gas is more consistent with clearing by giant planet formation than by photoevaporation or by grain growth. There is also an indication of global CO gas depletion in the disk, as the mass estimated from 13CO emission (∼3.8 × 10^(-4) M) is about two orders of magnitude lower than that derived from the 1.3 mm continuum (∼2.8 × 10^(-2) M).