We present CO J=4-3 line and 3 mm dust continuum observations of a 100 kpc-scale filamentary Ly{alpha} nebula (SSA22 LAB18) at z=3.1 using the Atacama Large Millimeter/submillimeter Array (ALMA). We detected the CO J=4-3 line at a systemic z(CO)=3.093 {pm} 0.001 at 11 {sigma} from one of the ALMA continuum sources associated with the Ly{alpha} filament. We estimated the CO J=4-3 luminosity of LCO(4-3)=(2.3pm0.2)x10^9 K km s^{-1} pc^2 for this CO source, which is one order of magnitude smaller than those of typical z>1 dusty star-forming galaxies (DSFGs) of similar far-infrared luminosity L(IR)~10^{12} Lsun. We derived a molecular gas mass of Mgas=(4.4^{+0.9}_{-0.6})x10^9 Msun and a star-formation rate of SFR=270pm160 Msun yr^{-1}. We also estimated a gas depletion time of {tau}(dep)=17pm10 Myr, being shorter than those of typical DSFGs. It is suggested that this source is in a transition phase from DSFG to a gas-poor, early-type galaxy. From ALMA to Herschel multi-band dust continuum observations, we measured a dust emissivity index {beta}=2.3pm0.2, which is similar to those of local gas-poor, early-type galaxies. Such a high {beta} can be reproduced by specific chemical compositions for interstellar dust at the submillimeter wavelengths from recent laboratory experiments. ALMA CO and multi-band dust continuum observations can constrain the evolutionary stage of high-redshift galaxies through {tau}(dep) and {beta}, and thus we can investigate dust chemical compositions even in the early Universe.
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