Chuckle when there's a row about a race (6)
I believe the answer is:
titter
'chuckle' is the definition.
(I've seen this before)
'a row about a race' is the wordplay.
'a row' becomes 'tier' (a tier is a row of things).
'about' indicates putting letters inside.
'a race' becomes 'tt'.
'tier' placed around 'tt' is 'TITTER'.
'when there's' acts as a link.
(Other definitions for titter that I've seen before include "Chuckle" , "Stifled giggle" , "A high-pitched nervous laugh" , "Silly little laugh" , "Half-suppressed laugh" .)