We have measured the 12C/13C interstellar ratio in the Coalsack, a prominent dark nebula in the southern sky, by means of high resolution (λ/δλ=6x104) observations of the λ4232A CH+ line in the direction of the star HD110432 (d≃0.31kpc). The collection of a total of 53 spectra of this star and of a reference bright star (α Vir) has allowed us to obtain a mean spectrum with signal-to-noise ratio ≃1500 at 1 σ level. We have detected the weak 13CH+ absorption well resolved from the 12CH+ line and derived a column density ratio =71±11 by means of line profile fitting with Voigt profiles. This result is in very good agreement with the few existing determinations of the column density ratio in other 4 clouds at d ≲0.5kpc. The isotopic ratio is remarkably constant along different directions of the local interstellar medium and has a mean value =67±3. This value is in good agreement with the most recent estimates of the 12C/13C ratio in the solar vicinity derived from CO and H2CO emission lines observed at radio frequencies.