Random poly(ethylene-co-1,4-cyclohexylenedimethylene terephthalate) and poly(ethylene-co-1,4-cyclohexylenedimethylene terephthalate)/organoclay nanocomposites were synthesized via in situ polymerization of terephthalic acid, ethylene glycol, 1,4-cyclohexane dimethanol, and aminosilane-modified Cloisite30B. An amorphous copolyester was produced with incorporating 30 mol% of 1,4-cyclohexane dimethanol in glycol part. Samples were characterized using Fourier transform spectroscopy, nuclear magnetic resonance, 13C-NMR and 1H-NMR, X-ray diffraction, transmission electron microscopy, differential scanning calorimetry, thermal gravimetric analysis, and dynamic mechanical thermal analysis. Intrinsic viscosities of samples were in the 0.51–0.55 dL/g range. A commercial organoclay was modified prior to add into the reactor. 1H-NMR and 13C-NMR spectra were applied to determine cis: trans isomer ratio of 1,4-cyclohexane dimethanol in polymer chains, Molar ratio of 1,4-cyclohexane dimethanol: ethylene glycol in polymer chains, degree of randomness, mean length of sequences, Mn, and Mark–Houwinks equation parameters. X-ray diffraction results of nanocomposites, including 0.5 and 1 wt% of organoclay, showed no peak in small angles, hence, modified organoclay presented exfoliated structure in polymer matrix. Differential scanning calorimetry analyses revealed that all samples were amorphous. Oxygen, nitrogen, and carbon dioxide diffusion rates in samples were investigated. Nanocomposite, including 3 wt% of organoclay, has about 60% less permeability in comparison to neat copolyester.