Magnetic-atom chains on superconductors can host Majorana zero modes, but in finite chains the two end modes generally hibridize and split away from zero energy. We show that Cr chains assembled atom-by-atom on the Bi-terminated surface of Bi2Pd enter a short-localization-length Shiba chain regime wthat strongly suppreesses this finite-size hybridization. Scanning tunneling spectroscopy reveals a chaing-leght-driven closing and reopening of the in-gap spectrum, followed by zero-bias modes localized at the chains ends. Green-function calculations reproduce the evolution and show an exchange of electorn-holec haracter across the transition. From the residual splitting we extract a localization length of about three atomic sites, explaining the stability of the zero-energy modes in experimentally accessible chains.