Bulk-Rashba spin splitting is forbidden in tetradymite topological insulators like Bi₂Se₃ or Bi₂Te₃, since their quintuple-layer stacking preserves inversion symmetry. We show that BiSbTeSe₂ escapes this restriction: in the Se-Bi-Se-Sb-Te sequence, the structure loses its inversion center, reducing the point group symmetry at Γ from D_3d to C₃ᵥ. First-principles density functional calculations with spin-orbit coupling show that this ordered structure retains bulk band inversion and a linearly dispersive surface state of a strong topological insulator. Additionally, its bulk bands acquire a pronounced linear-in-k spin splitting away from Γ. Fitting the conduction- and valence-band doublets to symmetry-constrained two-band k· p Hamiltonians, we extract intrinsic linear Rashba coefficients of α_CB≈2.66 eV Å and α_VB≈0.35 eV Å. The conduction-band value places ordered BiSbTeSe₂ among the strongest bulk-Rashba topological-insulator systems reported to date and approaches the coupling found in the benchmark polar Rashba semiconductor BiTeI. Sublattice ordering thus provides a route to giant bulk spin–momentum locking that coexists with protected topological surface states, offering a platform in which bulk-Rashba and topological surface contributions to spin and charge transport can be investigated within the same material.