Nick,
If you are referring to SCEL/SCL Arturo Benitez Intl Airport, Santiago de Chile, there is in fact a Jepp Cat III chart. It is on the same page, 21-1A, as the Cat II approach.
This page has one minimum for Cat II, RA 100ft, and one minimum for Cat IIIA, RA 50ft. For Cat IIIB there is a note that the fail passive minimum is RA 50ft, otherwise RA 0ft. We have a company requirement for the missed approach climb gradient to be not less that 5.0%.
There is a shed load of obstacles on the approach path but all are OK with a 3* approach slope so the Jepp charts say. From experience they look mighty close though!
Should you be referring to one of the many other "Santiagos" in the world I apologise for wasting your time.