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 state1. 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 possible2. For example, the low-temperature properties of heavy-fermion systems are dominated by antiferromagnetic spin Fluctuations, which have been considered theoretically3 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 mechanism4. Here we use tunnelling spectroscopy to investigate the superconducting order parameter of a uranium-based heavy-fermion superconductorÐepitaxial thin ®lms of UPd2Al3. Our observation of a strong-coupling feature in the tunnelling conductivity, combined with recent inelastic neutron scattering data13±15 strongly suggest a pairing interaction mediated by spin Fluctuations.