Circulating quickly around system, chocolate eggs initially in gut (8)
I believe the answer is:
visceral
'gut' is the definition.
(thesaurus)
'circulating quickly around system chocolate eggs initially' is the wordplay.
'circulating quickly' becomes 'viral' (something viral spreads quickly).
'around' means one lot of letters goes inside another.
'initially' indicates taking the first letters.
The first letters of 'system chocolate eggs' is 'sce'.
'viral' going around 'sce' is 'VISCERAL'.
'in' is the link.
(Other definitions for visceral that I've seen before include "Relating to deep feelings - claviers (anag)" , "Relating to deep inner feelings" , "Of the internal organs (esp. guts)" , "Instinctive, gut" , "Relating to gut reaction" .)