  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.
