  In the present work, we derive a linearly stable and causal theory of
relativistic third-order viscous hydrodynamics from the Boltzmann equation with
relaxation-time approximation. We employ viscous correction to the distribution
function obtained using a Chapman-Enskog like iterative solution of the
Boltzmann equation. Our derivation highlights the necessity of incorporating a
new dynamical degree of freedom, specifically an irreducible tensors of rank
three, within this framework. This differs from the recent formulation of
causal third-order theory from the method of moments which requires two
dynamical degrees of freedom: an irreducible third-rank and a fourth-rank
tensor. We verify the linear stability and causality of the proposed
formulation by examining perturbations around a global equilibrium state.
