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 1.1mm continuum source found in the AzTEC/JCMT survey (Scott et al. 2008), 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 $z=4.3420pm0.0004$ is confirmed by the detection of the redshifted 158 micron [C II] line using the Submillimeter Array. The new redshift and Herschel photometry yield $L_{FIR}=(1.1pm0.1)times 10^{13} L_odot$ and $SFR = 1300, M_odot$ yr$^{-1}$. Its molecular gas mass derived using the ULIRG conversion factor is $1.4pm0.2 times 10^{11} M_odot$ while the total ISM mass derived from the 1.1mm dust continuum is $3.7pm0.7 times 10^{11} M_odot$ assuming dust temperature of 35 K. Our dynamical mass analysis suggests that the compact gas disk ($rapprox 1.1$ kpc, inferred from dust continuum and SED 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 $L_{[C~II]} = 7.8pm1.1 times 10^9 L_odot$ 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 $Sigma_{FIR}$ among IR-bright galaxies reported by Diaz-Santos et al. (2013) 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.
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