Abstract We studied the reaction of doubly charged carbon C²⁺ (C iii) with molecular hydrogen, a possible source of the high, unexplained abundances of interstellar CH⁺. The experiment was carried out using the cryogenic linear 22-pole radio frequency ion trap. The measured reaction rate coefficient amounts to (1.5 ± 0.2) × 10⁻¹⁰ cm³ s⁻¹, nearly independently of the covered temperature range from 15 to 300 K. In the product distribution study, the C⁺ ion was identified as the dominant product of the reaction. For the CH⁺ production, we determine an upper limit for the reaction rate coefficient at 2 × 10⁻¹² cm³ s⁻¹.