We have observed a threshold in the electron photodetachment cross section of Sr ions at a photon energy hv = 1.820 eV and assign it to a p-wave transition from the 5s 5p P ground state in Sr to the Ss5p 3P state in neutral Sr. The measurement was made with a new technique combining the tunable laser photodetachment threshold method with accelerator mass spectrometry. We determine for the first time the electron affinity of Sr to be 48~6 meV, much smaller than predicted in recent calculations. The PI/2-P3/2 fine splitting of the Sr ground state is estimated to be 26~8 meV. PACS numbers: 32.10.Hq, 07.75.+h, 32.80.Fb Investigations of the stability of free negative ions provide excellent testing grounds for our understanding of the many-body problems of electrons bound to nuclei and the subtle electron correlation processes. The case of Ca, in particular, has become fascinating when, in contrast to former predictions, it was experimentally discovered to form a stable negative ion [1]. Confirmed by calculations, this state is described as a 4p electron bound to the Ca ground state to form a 4s 4p P configuration [2]. The electron affinity was then predicted to be 45 meV [2] (see also [3,4] for recent references) and measured as 43~7 meV [1]. Later experiments