The Josephson effect provides a direct method to probe the strength of the pairing interaction in superconductors. By measuring the phase fluctuating Josephson current between a superconducting tip of a scanning tunneling microscope (STM) and a BCS superconductor with isolated magnetic adatoms on its surface, we demonstrate that the spatial variation of the pairing order parameter can be characterized on the atomic scale. This system provides an example where the local pairing potential suppression is not directly reflected in the spectra measured via quasipartcile tunneling. Spectroscopy with such superconducting tips also show signatures of previously unex- A number of novel superconducting states of matter such as those appearing in disordered superconductors, heavy fermion materials, and high-T c superconductors have been predicted to have pairing order parameters that are spatially modulated on atomic length scales. These short range spatial modulations can occur due to different mechanisms such as the inhomogeneous material properties in disordered superconductors [1][2][3][4], a momentum dependent pairing interaction, such as the Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state proposed for heavy fermion materials [5][6][7], or the interplay between different forms of electronic ordering in the pair density waves proposed for high-T c cuprates [8][9][10]. Although spectroscopic mapping with a scanning tunneling microscope (STM) can provide evidence for variations in the local density of states (LDOS) through quasi-particle tunneling, such measurements probe the superconducting order parameter only indirectly. If the Josephson effect can be measured and mapped on the atomic scale, then it would allow for direct characterization of the local pairing order parameter and high-resolution studies of novel superconducting phases [11].This goal has motivated previous efforts in the use of superconducting tips in STM [12] and has led to the local observation of thermal phase fluctuating Josephson supercurrent close to the point contact regime [13][14][15]. Subsequent measurements have mapped the Josephson effect on the nanometer scale, applying this technique to vortices [16,17] and high-T c cuprates [18,19]. A major challenge in improving the resolution of these experiments has been satisfying the competing requirements of a high junction impedance necessary for imaging and a low junction impedance allowing for the strong tip-sample coupling necessary to observe the Josephson effect despite thermal fluctuations. Extending the Josephson STM measurements to millikelvin temperatures allows for mapping of the Cooper pair current at junction resistances that are compatible with atomic resolution imaging.In this letter, we use scanning Josephson spectroscopy to probe variations of the superconducting order parameter on the scale of a single atom. We map the strength of the phase fluctuating Josephson current between a superconducting Pb tip and a Pb(110) surface with a dilute concentration of magnetic impurities us...