We present spatially-resolved properties of molecular gas and dust in a gravitationally-lensed submillimeter galaxy H-ATLAS J090311.6+003906 (SDP.81) at $z=3.042$ revealed by the Atacama Large Millimeter/submillimeter Array (ALMA). We identified 14 molecular clumps in the CO(5-4) line data, all with a spatial scale of $sim$50-300 pc in the source plane. The surface density of molecular gas ($Sigma_{rm H_2}$) and star-formation rate ($Sigma_{rm SFR}$) of the clumps are more than three orders of magnitude higher than those found in local spiral galaxies. The clumps are placed in the `burst sequence in the $Sigma_{rm H_2}$-$Sigma_{rm SFR}$ plane, suggesting that $z sim 3$ molecular clumps follow the star-formation law derived for local starburst galaxies. With our gravitational lens model, the positions in the source plane are derived for the molecular clumps, dust clumps, and stellar components identified in the {sl Hubble Space Telescope} image. The molecular and dust clumps coexist in a similar region over $sim$2 kpc, while the stellar components are offset at most by $sim$5 kpc. The molecular clumps have a systematic velocity gradient in the north-south direction, which may indicate a rotating gas disk. One possible scenario is that the components of molecular gas, dust, and stars are distributed in a several-kpc scale rotating disk, and the stellar emission is heavily obscured by dust in the central star-forming region. Alternatively, SDP.81 can be explained by a merging system, where dusty starbursts occur in the region where the two galaxies collide, surrounded by tidal features traced in the stellar components.
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