Chaves, second overall in 2016, sat second in the general classification behind British team-mate and race leader Simon Yates when stage 10 left Abruzzo after the rest day. He finished the race's longest day, 244 kilometres, six-and-a-half hours later.
Dropped in the opening kilometres of the stage, Chaves fought to rejoin, but failed. He crossed the line 25 minutes behind and drifted to 39th overall.
Attention now turns to Yates's overall hopes. Chaves and the team will rally behind him as he attempts to win the grand tour ahead of stars Chris Froome (Team Sky) and Tom Dumoulin (Team Sunweb).
"We've still got to understand my problems," Chaves said.
"I just didn't have the strength and couldn't stay with the best on the first climb. We tried to chase with the team and got to within one minute, but it didn't work out."
Chaves enjoyed the rest day with Yates, sitting shotgun to the race leader with two weeks left. The first climb out of the start town of Penne, though, finished his Giro hopes.
Teams were ready, too. Mitchelton and other teams warmed up on turbo trainers given the hard start predicted. Chaves and Sports Director Matt White had even driven the first 100 kilometres on the rest day.
Yates, as he has since the race started in Jerusalem, rode like a cyclist on the verge of winning his first grand tour. Chaves paid, however, through the tough hills of Abruzzo, Marche and Umbria. White guessed that allergies affected him.
With Chaves now clearly out of the overall picture, any question of team leadership is answered.
"I'm confident that I'm going well, I have great legs, but not going to think this is going to be easy. My rivals are extremely strong. I'm confident, but I understand what I'm trying to achieve," Yates said.
"I think it becomes harder, because we are on the final climbs and before, we had two cards to play.
"Now it's only me and we'll have to adjust. For sure he'll be a strong help for me in the climbs, so you can look at it two ways."
"Nothing changes, we're still trying to win the Giro," White explained.
"Esteban's chances for GC are gone, which means I've got one very handy helper for Simon when it matters. We're only back to the same square as every other team now."
Thank you for reading 20 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1