We computationally study the thermoelectric performance of the orthorhombic (Pnma) barium chalcogenide perovskites BaAX3 (A = Zr, Hf; X = S, Se) using a first-principles framework that couples the self-consistent phonon theory with Boltzmann transport. Higher-order interatomic force constants were computed using a machine-learning sparse-regression approach (LASSO) as implemented in the ALAMODE code [1, 2]. Explicit anharmonic lattice dynamics then accounts for strong phonon–phonon scattering and temperature-induced phonon renormalization, removing dynamical instabilities in Zr-based compounds and strongly suppressing lattice thermal conductivity κl. As a result, we obtain ultralow values such as κavgl ≈ 0.43 W·m−1·K−1 at 900 K for BaHfSe3. Electronic transport properties (S, σ, κe) are computed by explicitly accounting for acoustic-deformation, polar optical phonons, and ionized-impurity scattering mechanisms. Among the four compounds, n-type BaHfSe3 delivers the best performance, reaching ZT ≈ 1.1 at 900 K, driven by its suppressed κl and a large power factor (P F ≈ 1.3 mW·m−1·K−2). Overall, our computations highlight Ba-based chalcogenide perovskites, especially the Se-rich members, as strong candidates for high-temperature thermoelectric energy conversion.