The destruction of CH+ ions in collisions with H atoms has been studied in a temperature-variable 22 pole ion trap (22PT) combined with a cold effusive H-atom beam. The stored ions are relaxed to temperatures of T 22PT >= 12 K. The hydrogen atoms, produced in a radio frequency discharge, are slowed down to various temperatures of T ACC >= 7 K. They are formed into an effusive beam. The effective density of the hydrogen atoms in the trap as well as the H2 background are determined in situ using chemical probing with CO2 +. The experimental arrangement allows us not only to measure thermal rate coefficients (T 22PT = T ACC), but also to extract state-specific rate coefficients k(J,T t) at selected translational temperatures T t and for the CH+ rotational states J = 0, 1, and 2. The measured thermal rate coefficients have a maximum at 60 K, k = (1.2 ? 0.5)X10--9 cm3 s--1. Toward higher temperatures, they fall off in accordance with previous measurements and the trend predicted by phase space theory. Toward lower temperatures, the rate coefficients decrease significantly, especially if the rotation of the ions is cooled. At the coldest conditions achieved (beam: 7.3 K; trap: 12.2 K), a value as low as (5 ? 4) X 10--11 cm3 s--1 has been measured. This leads to the conclusion that non-rotating CH+ is protected against attacks of H atoms. This surprising result is not yet understood. It is most probably due to quantum-dynamical effects already occurring at large distances.