I don't think that, the overall few times Chiello does ever make a big mistake in defense, it's fault of the 3-men backline. At all. I think that the 3-men defence actually suits him really well for the standards of a defender, even in the runs forward, he has a good timing and can understand when to track back, and is quite fast to do it (infact he borns as LB and he's played in that position until he was like 23).
Let's not also forget that in the first year with Conte, Chiellini started horribly with the 4-man backline, fucking up in many matches (Bologna, Catania, Genoa, just the first ones that come to my mind, in the first part of the season), and was highly criticized (I remember people talking about a Barzagli-Bonucci partnership, and Leo was criticized too, so...), but in the 3-men backline his performances improved. He has had some fucks-up in the last season though, especially in the NT (where Prandelli used the 4 man defence, lol), but he had still overall a fantastic season and he's still one of the best in the world, no doubts about it. If we've had the best defence three years in a row it's not just due to (the great) Barzagli. He's a bit over-criticized for his clumsy style, but if Chiello wouldn't be here, even with some over-hyped young defender, we would feel the difference.