Strong acoustic phonon suppression leads to ultralow thermal conductivity and enhanced thermoelectric performance in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Ba</mml:mi><mml:mi>Cu</mml:mi><mml:mi>Gd<

Finding crystalline semiconductors with intrinsically low lattice thermal conductivity ${\ensuremath{\kappa}}_{l}$ is crucial for thermoelectric applications, as tuning ${\ensuremath{\kappa}}_{l}$ often compromises electrical transport properties. Using density functional theory, Boltzmann transport theory, and explicit consideration of phonon-phonon and electron-phonon interactions, the authors show that BaCuGdTe${}_{3}$ exhibits ultralow ${\ensuremath{\kappa}}_{l}$, due to its layered structure and local distortions that strongly suppress acoustic phonon modes, and excellent electrical transport properties, due to strong covalent bonding within its layers. These results can be used as a basis for designing compounds with ultralow ${\ensuremath{\kappa}}_{l}$.