Surface limited redox replacement (SLRR) is an electrochemical deposition method designed to deposit metal thin films, typically onto other metals, that are mere monolayers in thickness, where such low dimensions allows catalyst-support interactions to affect catalyst efficiency. Here we explore the growth of Pt, using iterative Cu-mediated SLRR cycles, directly onto carbon nanotubes (CNTs) which are potentially good candidates as electrocatalyst supports due to their electrical conductivity and chemical resistance. Scanning electron microscope images showed that Pt grew as nanoparticles, and hydrogen underpotential deposition from cyclic voltammetry showed that the active surface area approached an asymptotic value around eight iterations. Catalytic activity, measured using the oxygen reduction reaction, reached a maximum at ten iterations. Both are shown to be influenced by the growth mode, but electrochemical modeling indicates that the trend in activity is also due to a change in activation energy, possibly due to changes in Pt electronic structure due to interactions with the CNTs. Durability cycling showed a greater than 85% retention of surface area for the first 10,000 cycles of accelerated stress testing but decayed steadily to about 50% after 30,000 cycles. This performance may be related to the phenomenon that limits surface area growth.