  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 L'CO(4-3)=(2.3\pm0.2)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=270\pm160 Msun yr^{-1}. We also estimated a gas
depletion time of {\tau}(dep)=17\pm10 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}=2.3\pm0.2, 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.
