This photograph turned up on E-Bay, just after a fortuitous donation from one of my other blogs arrived at my PayPal account. It was made by North and Oswald, "Photographic Artists" in the Hall Block, at Jefferson and St. Clair. The Hall Block was built in 1875 and destroyed by fire in 1882. That provides a convenient way to assign a date.
Now, the question of who the priest might be. Judging by the nose and the shape of the face, I'm 90% certain it's Fr. Patrick O'Brien, founder of Good Shepherd Parish and second pastor of Immaculate Conception. Two people I asked agree. Fr. O'Brien was ordained in 1872, and was at Good Shepherd and Immaculate Conception throughout the period between 1875 and 1889, so the time frame fits as well.
The mystery of the matter? Where's it been since? I bought it, for less than I ever would have expected ( 99 cents ) from a dealer on the West Coast.