The Doppler-limited FTIR spectrum of the band system in the region 1070-1170 cm(-1) (Doppler width approximate to0.0015 cm(-1), FWHM) was measured with our new Bruker IFS 120 HR Zurich prototype (ZP2001) spectrometer. This instrument allows for an unapodized resolution of 0.0007 cm(-1) (FWHM). This is the highest resolution realized so far by a commercial FTIR spectrometer system. It allows high-resolution analysis of the room temperature spectra of the strongly coupled modes nu(3)(a') and nu(8)(a"), corresponding to the symmetric and antisymmetric CF-stretching vibrations, including also further couplings not analysed previously. The present analysis is based on effective rotational Hamiltonians for the nu(3) = 1 and nu(8) = 1 states, including all terms up to sextic, and involves the full first-order Coriolis interaction operator (H) over cap (3,8)(Coriolis) = ixi(a)(3,8) (J) over cap (a) + ixi(c)(3,8) (J) over cap (c). Consideration of both the (J) over cap (a) and (J) over cap (c) first-order Coriolis terms proved essential in order to obtain good line-by-line agreement between observed and calculated rovibrational structures over the full band system. In addition, the analysis of two local resonances allowed us to determine the vibrational wavenumbers of the 3nu(9) and nu(6) + 2nu(9) levels with good accuracy. We describe possible approaches to the analysis. The final analysis involves both chlorine isotopomers and includes all hybrid components which are allowed by symmetry. It results in the band centres nu(3)(0) = 1108.7274 cm(-1), nu(8)(0) = 1127.282 cm(-1), 3nu(9)(0) = 1098.5 cm(-1) and (nu(6) + 2nu(9))(0) = 1144.32 cm(-1), where the last digit is rounded, relating to the first digits differing in two types of analyses and data sets from our work. The main Coriolis interaction parameters are xi(a)(3,8) = 0.385 cm(-1) and xi(c)(3,8) = -0.095 cm(-1). In addition, smaller interactions could also be determined quantitatively. Our results are in essential agreement with the original analysis of Luckhaus and Quack (1989, Molec. Phys., 68, 745), which was, however, much less complete and precise. We discuss the comparison of different types of analyses and further recent results on this band system. We report ab initio calculations for this molecule on the MP2 level of theory with an aug-cc-pVDZ or an aug-cc-pVTZ basis set. Various subspaces of the potential energy and electric dipole moment hypersurface have been calculated in reduced normal coordinates including up to three dimensions. With these hypersurfaces we determined the corresponding vibrational absorption spectra, comprising transition wavenumbers and intensities. An analysis of the vibrational levels with an effective Hamiltonian was used to derive anharmonic constants. We also derived Coriolis coupling constants and integrated absorption intensities ab initio, which are compared with the present and previous experimental and theoretical results. The complete set of data as analysed is tabulated in Appendix A of this publication [61].