  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.
