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We investigate the in-plane thermal conductivity (κ) of quasi two-dimensional honeycomb magnet CrCl₃, as a function of temperature (T) and applied field (H). In contrast to isomorphic cousin RuCl₃, spin-orbit coupling in CrCl₃, is expected to be weak, providing a window into phonon-related contributions to thermal transport. We find that in-plane κ is insensitive to the applied field direction, either in the ab-plane or along the c axis, supporting the assertion that spin-orbit coupling plays a minimal role. However, a large, non-saturating enhancement of κ(H) up to H = 18 T for a range of T as high as 60 K, suggests a strong suppression of spin-phonon scattering under applied field. We will discuss estimations of the phonon contribution to κ, and compare to the case of RuCl₃.