The rotational structure in the vibrational transitions from ν=0 to ν=1,2,3,4 of H³⁵Cl and H³⁷Cl is studied in Xe, Kr and Ar matrices with high spectral resolution. A consistent set of rotational constants B_v for the vibrational levels ν=0 to 4 is derived. B₀ decreases with the tightness of the cage from 9.78 cm^-1 in Xe to 8.83 cm^-1 in Ar for H³⁵Cl (gas phase 10.44 cm^-1). The values for B₀ to B₄ decrease linearly with v due to the vibration-rotation-coupling constant α which increases from 0.37 cm^-1 in Xe to 0.479 cm^-1 in Ar (gas 0.303) according to the cage tightness. The splitting of the R(1) transition which originates from the hindering of rotation is analyzed in Xe using the T_2g-T_1u and T_2g-E_g transition energies. A comparison with force field calculations yields a dominant contribution of the 6th spherical harmonic Y_A1g⁶ of the octahedral matrix potential. The modulation of the potential takes a value of K₆/B=17 which corresponds to a barrier for the rotation of 160 cm^-1. The splitting increases with the vibrational level v which can be interpreted as a weak admixture of the Y_A1g⁴ spherical harmonic. A large isotope effect and a reduction of the T_1u-A_1g transition energy (R(0)-transition) beyond the crystal field value are attributed to an excentric rotation with a displacement of the center of mass of the order of 0.05 Å. The vibrational energies ωe show an opposite trend with matrix atom size and decrease with polarizability from 2970 cm^-1 in Ar to 2945.4 cm^-1 in Xe (gas 2989.9 cm^-1) while the anharmonicity ω_eχ_e of the free molecule lies close to the Kr value and thus between that of Ar and Xe.