Use an armor stand to follow the egg and summon chicks when the armor stand loses the snowball.
Setup:
/scoreboard objectives add Stand dummy
/scoreboard objectives add hasStand dummy
/scoreboard objectives add hasEgg dummy
Clock:
/scoreboard players set @e[type=ArmorStand] Stand 1 {Marker:1,Invisible:1,NoGravity:1}
/execute @e[type=ThrownEgg,score_hasStand_min=1] ~ ~ ~ tp @e[type=ArmorStand,score_Stand_min=1,c=1] @e[type=ThrownEgg,score_hasStand_min=1,c=1,r=1]
/scoreboard players set @e[type=ThrownEgg] hasStand 0
/scoreboard players set @e[type=ArmorStand,score_Stand_min=1] hasEgg 0
/execute @e[type=ArmorStand,score_Stand_min=1] ~ ~ ~ scoreboard players set @e[type=ThrownEgg,r=1,c=1] hasStand 1
/execute @e[type=ThrownEgg,r=1,c=1] ~ ~ ~ scoreboard players set @e[type=ArmorStand,score_Stand_min=1] hasEgg 1
/execute @e[type=ThrownEgg,score_hasStand=0] ~ ~ ~ summon ArmorStand ~ ~ ~ {Marker:1,Invisible:1,NoGravity:1}
/scoreboard players @e[type=ThrownEgg] hasStand 1
/execute @e[type=ArmorStand,score_Stand_min=1,score_hasEgg=0] ~ ~ ~ summon Chicken ~ ~ ~ {Age:-400}
/kill @e[type=ArmorStand,score_Stand_min=1,score_hasEgg=0]