Chicken to shout 'that hurt!' (6)
I believe the answer is:
yellow
'chicken' is the definition.
(as in cowardly)
'shout that hurt' is the wordplay.
'shout' becomes 'yell' (synonyms).
'that hurt' becomes 'ow' (exclamation of pain).
'yell'+'ow'='YELLOW'
'to' is the link.
(Other definitions for yellow that I've seen before include "Sunny colour" , "like a canary" , "Colour of egg yolk and cowardice" , "egg is partly this" , "Offensively sensational" .)