Teetotaller in drunken rite gives chuckle (6)
I believe the answer is:
titter
'chuckle' is the definition.
(I've seen this before)
'teetotaller in drunken rite' is the wordplay.
'teetotaller' becomes 'tt' (abbreviation).
'in' is an insertion indicator.
'drunken' indicates anagramming the letters.
'rite' is an anagram of 'tier'.
'tt' inserted inside 'tier' is 'TITTER'.
'gives' acts as a link.
(Other definitions for titter that I've seen before include "Chuckle" , "Half-suppressed laugh" , "Nervously restrained laugh" , "A high-pitched nervous laugh" , "Nervous restrained laugh" .)