Measuring redshifted CO line emission is an unambiguous method for obtaining an accurate redshift and total cold gas content of optically faint, dusty starburst systems. Here, we report the first successful spectroscopic redshift determination of AzTEC J095942.9 022938 (`COSMOS AzTEC-1'), the brightest 1.1 mm continuum source found in the AzTEC/James Clerk Maxwell Telescope survey (Scott et al.), through a clear detection of the redshifted CO (4-3) and CO (5-4) lines using the Redshift Search Receiver on the Large Millimeter Telescope. The CO redshift of z = 4.3420 ± 0.0004 is confirmed by the detection of the redshifted 158 µm [C II] line using the Submillimeter Array. The new redshift and Herschel photometry yield LFIR = (1.1 ± 0.1) × 1013 L? and SFR ˜ 1300 M? yr-1. Its molecular gas mass derived using the ultraluminous infrared galaxy conversion factor is 1.4 ± 0.2 × 1011M? while the total interstellar medium mass derived from the 1.1 mm dust continuum is 3.7 ± 0.7 × 1011M? assuming Td = 35 K. Our dynamical mass analysis suggests that the compact gas disc (r ˜ 1.1 kpc, inferred from dust continuum and spectral energy distribution analysis) has to be nearly face-on, providing a natural explanation for the uncommonly bright, compact stellar light seen by the HST. The [C II] line luminosity L_[C II]= 7.8± 1.1 × 10^9 L_{?} is remarkably high, but it is only 0.04 per cent of the total IR luminosity. AzTEC COSMOS-1 and other high redshift sources with a spatially resolved size extend the tight trend seen between [C II]/FIR ratio and SFIR among IR-bright galaxies reported by Díaz-Santos et al. by more than an order of magnitude, supporting the explanation that the higher intensity of the IR radiation field is responsible for the `[C II] deficiency' seen among luminous starburst galaxies.
