Underground chamber opening in California state institution at last (6)
I believe the answer is:
cavern
'underground chamber' is the definition.
(I've seen this before)
'opening in california state institution at last' is the wordplay.
'opening in' says to take the initial letters.
'state' becomes 'aver' (both can mean to declare).
'at last' says to take the final letters.
The initial letter of 'california' is 'c'.
The final letter of 'institution' is 'n'.
'c'+'aver'+'n'='CAVERN'
(Other definitions for cavern that I've seen before include "vast enclosed space" , "Subterranean chamber" , "Large dark hole in the ground" , "Grotto" , "Liverpool club where The Beatles started out" .)