Using Chandra data taken in 2008 June, we detected pulsations at 2.594 39(4) s in the soft gamma-ray repeater SGR 1627−41. This is the second measurement of the source spin period and allows us to derive for the first time a long-term spin-down rate of (1.9 ± 0.4) × 10−11 s s−1. From this value, we infer for SGR 1627−41 a characteristic age of ∼2.2 kyr, a spin-down luminosity of ∼4 × 1034 erg s−1 (one of the highest among sources of the same class), and a surface dipole magnetic field strength of ∼2 × 1014 G. These properties confirm the magnetar nature of SGR 1627−41; however, they should be considered with caution since they were derived on the basis of a period derivative measurement made using two epochs only, and magnetar spin-down rates are generally highly variable. The pulse profile, double-peaked and with a pulsed fraction of 13 ± 2 per cent in the 2–10 keV range, closely resembles that observed by XMM–Newton in 2008 September. Having for the first time a timing model for this soft gamma-ray repeater (SGR), we also searched for a pulsed signal in archival radio data collected with the Parkes radio telescope 9 months after the previous X-ray outburst. No evidence for radio pulsations was found, down to a luminosity level ∼10–20 times fainter (for a 10 per cent duty cycle and a distance of 11 kpc) than the peak luminosity shown by the known radio magnetars.