We have undertaken an extensive calculation to obtain the oscillator strengths for all optically allowed and intercombination E1 transitions in Cl I between the fine-structure levels of the odd-parity configurations 3s²3p⁵, 3p⁴(¹D)4p, 3p⁴(³P)np(4 ≤ n ≤ 5) and the even-parity configurations 3s3p⁶, 3p⁴(³P, ¹D, ¹S)ns(4 ≤ n ≤ 5), 3p⁴(³P)6s, 3p⁴(³P, ¹D)3d, 3p⁴(³P)4d, within the Breit–Pauli approximation, using the method of interaction of configurations (CI) enveloped in the general atomic structure code CIV3. The CI wavefunctions have been constructed from a common orthogonal set of 23 one-electron functions (OEFs), which have been carefully selected to ensure that the LS dependency of the orbitals and all important correlation effects have been accurately represented. In the LS-coupling regime, the configuration state functions (CSFs) included in the atomic wavefunction expansions were obtained from all single- and double-electron replacements to the OEFs for each symmetry from the orbitals in the set of dominant configurations 3s²3p⁵, 3s3p⁶, 3s²3p⁴nl. At the LSJ stage we retain only those CSFs with eigenvector components ≥0.0005 in magnitude. We then make a further ad hoc refinement to the calculation, whereby the diagonal Hamiltonian matrix elements are adjusted so that the theoretical energy differences coincide with the relevant experimental values. Alternative energy level classifications are proposed for a number of heavily mixed J = 5/2 and J = 3/2 levels based on our calculations, and are supported by the experimental measurements of Schectman et al (1993 Astrophys. J. 406 735). Our results are compared with experimental and available theoretical data. We observe excellent agreement in the length and velocity forms of the oscillator strengths, demonstrating a marked improvement over previous work by Ojha and Hibbert (1990 Phys. Scr. 42 424) and Singh et al (2006 Eur. Phys. J. D 38 285). We predict new oscillator strength data for transitions involving the 3p⁴(³P)5p, 3p⁴(³P)4d, 3p⁴(³P)6s configurations where no other theoretical values are available.