In America very deep chamber (4)
I believe the answer is:
cave
'chamber' is the definition.
(I have seen 'Underground chamber' mean 'cave' so perhaps 'chamber' could also mean 'cave')
'in america very deep' is the wordplay.
'in' indicates a hidden word.
'CAVE' is hidden in the letters of 'america very deep'.
(Other definitions for cave that I've seen before include "Watch out" , "Primitive dwelling" , "Hollow - warning" , "Warning - grotto" , "Large grotto" .)