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 ( 69 ) , 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 \pm 0.0004 is confirmed by the detection of the redshifted 158 \mu m [ C II ]  line using the Submillimeter Array . The new redshift and Herschel  photometry yield L _ { FIR } = ( 1.1 \pm 0.1 ) \times 10 ^ { 13 } L _ { \odot } and SFR \approx 1300 M _ { \odot } yr ^ { -1 } . Its molecular gas mass derived using the ULIRG conversion factor is 1.4 \pm 0.2 \times 10 ^ { 11 } M _ { \odot } while the total ISM mass derived from the 1.1mm dust continuum is 3.7 \pm 0.7 \times 10 ^ { 11 } M _ { \odot } assuming T _ { d } = 35 K. Our dynamical mass analysis suggests that the compact gas disk ( r \approx 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 ] } = 7.8 \pm 1.1 \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 Díaz-Santos et al . ( 19 ) 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 .