Using an unusually large high-frequency dataset, this paper seeks to investigate the mechanism by which the Law of One Price (LOP) can be enforced between UK shares and their American Depository Receipts (ADRs). On the one hand, existing works show that pure-arbitrage strategies (i.e. conversion of ADRs into underlying shares or vice versa) rarely materialise due to the associated costs and regulatory constraints, favouring price efficiency. However, this notion is at odds with other strands of the literature and the industry perspective which often cite the stock-ADR environment as a heavily-arbitraged market. Our research proposes to reconcile these two views by presenting a hitherto unexamined mechanism by which the LOP in this market can be enforced, namely pairs-trading. Using a comprehensive sample of UK stock-ADR pairs, we show that simple, unleveraged trading rules yield stable annual returns of 3-4% after adjusting for taxes, costs, and margin requirements. Interestingly, of the many inhibitors to arbitrage catalogued in the literature, we find transaction costs to be far more prevalent than idiosyncratic risks, contrary to similar environments such as dual-listed security pairs. These results are useful both in understanding the extent to which arbitrage is successful at eliminating stock-ADR mispricings, and the barriers which act as the limits to arbitrage.