Equilibrium statistical mechanics owes much of its analytical tractability to symmetry: detailed balance, gradient dynamics, and the resulting vanishing of steady-state entropy production are properties that follow directly from the structure of the underlying dynamics, not from any smallness of the perturbation. Exact solutions of this kind are rare away from equilibrium. Here we identify and characterize a class of far-from-equilibrium colloidal chains – coupled through roto-translational and autophoretic interactions – that, for a specified set of bilaterally-symmetric initial conditions, nevertheless admit an exact description. For fixed chain geometries, the monomer orientational dynamics map directly onto a scalar potential. Detailed balance holds strictly within the orientational sector, causing its steady-state entropy production rate (EPR) to vanish identically despite the system being manifestly driven and dissipative. We solve these reduced dynamics exactly for dimers and semi-analytically for general $N$-mers, deriving closed-form expressions for mean-squared orientational fluctuations and total EPR. Crucially, this exact mapping demonstrates that, at fixed chain geometry, all non-equilibrium entropy production is strictly partitioned into the translational (center-of-mass) sector. Extending the framework to incorporate dipolar chemical emission reveals that while dimers retain this quasi-equilibrium structure, longer chains ($N>2$) break it completely—generating a genuinely non-equilibrium state whose EPR fails to reach a steady state. Monopolar coupling is thus both necessary and sufficient to sustain the polarized quasi-equilibrium state, establishing explicit physical boundaries for exact thermodynamic descriptions of active colloidal chains.