A new triclinic layered borate, |Ag₄Br|@[B₇O₁₂], has been prepared by glass crystallization and slow cooling stoichiometric melts in evacuated silica ampoules. The structure is based upon a layered borate anion 7:∞² [(4: 2Δ + 2 T) + (3: 2Δ + T)] with an architecture yet not observed among inorganic borates. The layers consist of two parts comprised of tri- and tetraborate groups; it is ∼7 Å thick and oriented parallel to (001). The interlayer space is filled by the cationic [Ag₄Br]³⁺sublattice exhibiting disorder and anharmonicity at the silver sites. The new compound was characterized by thermal analysis, high-temperature powder X-ray diffraction, vibrational and UV–Vis–NIR spectroscopy, as well as DFT calculations. For the triclinic unit cell, the eigenvalues of the thermal expansion tensor and the orientation of the thermal expansion tensor relative to the crystallographic axes are determined. The thermal expansion of the new borate bromide is strongly anisotropic, being marginal in the plane of the B–O layers (α₁₁ = 8.2 (1), α₂₂ = 4.71 (3) × 10⁻⁶ °С⁻¹) while quite large in the normal direction (α₃₃ = 38.2 (3) × 10⁻⁶).