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 +/- 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 +/- 0.2) x 10(9) Kkms(-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 similar to 10(12) L-circle dot. We derived a molecular gas mass of M-gas = (4.4(-0.6)(+0.9)) x 10(9) M-circle dot and a star-formation rate of SFR = 270 +/- 160M(circle dot) yr(-1). We also estimated a gas depletion time of tau(dep) = 17 +/- 10 Myr, which is shorter than those of typical DSFGs. It is suggested that this source is in the 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 +/- 0.2, which is similar to those of local gas-poor, early-type galaxies. From recent laboratory experiments, the specific chemical compositions needed to reproduce such a high beta for interstellar dust at the submillimeter wavelengths. 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 the chemical composition of dust even in the early Universe.