There has been some discussion recently about where you will do the customs check, Frankfurt or Santiago. It would pay to check with your airline whether you are doing that at FRA and transferring to an internal flight, or you remain on an international flight, and on the transit in FRA, you don't need to collect your baggage and then have to clear customs at SCQ.
I have seen both patterns at Schengen zone airports, but haven't been through Frankfurt. Those who have are optimistic that flights from the US are treated as international flights through to their final destination.
That said, as
@henrythedog suggests, you will only have to clear customs once, at least in Europe. There are different arrangements in the US, where transit passengers need to collect and clear their baggage, and then re-check it for the next leg(s) of their flight.