We investigate the mobility of one-dimensional n-adatom chains deposited on the (110)(1x2) metal surface. All known diffusion mechanisms are taken into account; dissociation-reassociation processes are also included. On the missing-row reconstructed surface, diffusion may proceed via the leapfrog mechanism. Through a set of analytical calculations we find the law describing leapfrog-induced diffusion for every n. It turns out that in a wide range of n, at typical experimental temperatures, chain mobility may be independent of the chain length. As a consequence, even long chains are expected to display a significant mobility. On the contrary, on the (110)(1x1) surfaces, where the leapfrog diffusion mechanism is not present, tetramers are already practically motionless.