It is well known that any weak attractive electron-electron interaction in metals can in principle cause the formation of Cooper pairs, which then condense into a superconducting ground state(1). In conventional superconductors, this attractive interaction is mediated by lattice vibrations (phonons). But for the heavy-fermion and high-temperature superconductors, alternative pairing interactions are considered to be possible(2). For example, the low-temperature properties of heavy-fermion systems are dominated by antiferromagnetic spin fluctuations, which have been considered theoretically(3) as a possible cause for Cooper-pair formation. This picture recently received some experimental support: the resistivity behaviour under pressure of two cerium-based heavy-fermion compounds was shown to be consistent with a magnetically mediated pairing mechanism(4). Here we use tunnelling spectroscopy to investigate the superconducting order parameter of a uranium-based heavy-fermion superconductor-epitaxial thin films of UPd2Al3. Our observation of a strong-coupling feature in the tunnelling conductivity, combined with recent inelastic neutron scattering data(13-15) strongly suggest a pairing interaction mediated by spin fluctuations.