We present detections of the CO(4-3) and [C I] 609 $mu$m spectral lines, as well as the dust continuum at 480.5 GHz (rest-frame), in 3C 368, a Fanaroff-Riley class II (FR-II) galaxy at redshift (z) 1.131. 3C 368 has a large stellar mass, ~ 3.6 x 10$^{11}$ M$_odot$, and is undergoing an episode of vigorous star formation, at a rate of ~ 350 M$_odot$/yr, and active galactic nucleus (AGN) activity, with radio-emitting lobes extended over ~ 73 kpc. Our observations allow us to inventory the molecular-gas reservoirs in 3C 368 by applying three independent methods: (1) using the CO(4-3)-line luminosity, excitation state of the gas, and an $alpha_{CO}$ conversion factor, (2) scaling from the [C I]-line luminosity, and (3) adopting a gas-to-dust conversion factor. We also present gas-phase metallicity estimates in this source, both using far-infrared (FIR) fine-structure lines together with radio free-free continuum emission and independently employing the optical [O III] 5007 A and [O II] 3727 A lines (R$_{23}$ method). Both methods agree on a sub-solar gas-phase metallicity of ~ 0.3 Z$_odot$. Intriguingly, comparing the molecular-gas mass estimated using this sub-solar metallicity, M$_{gas}$ ~ 6.4 x 10$^{10}$ M$_odot$, to dust-mass estimates from multi-component spectral energy distribution (SED) modeling, M$_{dust}$ ~ 1.4 x 10$^8$ M$_odot$, yields a gas-to-dust ratio within ~ 15% of the accepted value for a metallicity of 0.3 Z$_odot$. The derived gas-mass puts 3C 368 on par with other galaxies at z ~ 1 in terms of specific star-formation rate and gas fraction. However, it does not explain how a galaxy can amass such a large stellar population while maintaining such a low gas-phase metallicity. Perhaps 3C 368 has recently undergone a merger, accreting pristine molecular gas from an external source.
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