The current chapel was being built in 1905, and the first service was held there in 1908. You can make out the original terracotta on the dome, there.
In 1922, the new bandstand was built in front of the chapel, but would not be seen from this view.
If that is Herndon in the photo, then the the bandstand would be to the left, out of frame. AND if that is indeed Herndon, then the extension of the chapel hasn't happened yet, which puts the photo before 1940. In a 1924 map of USNA, there is no tennis court shown in this position, in front of the chapel. If the map is correct, then the photo could have been taken any time between 1925 and 1939.