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Abstract Side‐arm hydrogenation (SAH) by homogeneous catalysis has extended the reach of the parahydrogen enhanced NMR technique to key metabolites such as pyruvate. However, homogeneous hydrogenation requires rapid separation of the dissolved catalyst and purification of the hyperpolarised species with a purity sufficient for safe in‐vivo use. An alternate approach is to employ heterogeneous hydrogenation in a continuous‐flow reactor, where separation from the solid catalysts is straightforward. Using a TiO₂‐nanorod supported Rh catalyst, we demonstrate continuous‐flow parahydrogen enhanced NMR by heterogeneous hydrogenation of a model SAH precursor, propargyl acetate, at a flow rate of 1.5 mL/min. Parahydrogen gas was introduced into the flowing solution phase using a novel tube‐in‐tube membrane dissolution device. Without much optimization, proton NMR signal enhancements of up to 297 (relative to the thermal equilibrium signals) at 9.4 Tesla were shown to be feasible on allyl‐acetate at a continuous total yield of 33 %. The results are compared to those obtained with the standard batch‐mode technique of parahydrogen bubbling through a suspension of the same catalyst.