The Colombian's debut Tour has veered far from the script that was written at the start of the year, and based on his extraordinary 2016 campaign in which he finished on the final podium of both the Giro d'Italia and Vuelta a España. Chaves is set to finish the Tour in 63rd place, almost two-and-a-half hours down on Chris Froome, but these have been a complicated three weeks for a number of reasons.
First of all, his preparation was disrupted by a knee injury that he picked up in February and that kept him out of action until June. Then, just two days into the Tour, came a huge emotional hit, as he found out his close friend and physiotherapist, who helped him back from his horrific 2013 injury, Diana Casas had tragically died in a road accident.
"We came to the Tour not knowing where he was going to be at, with his lack of racing, then obviously things got a bit more complicated with the death of his friend and staff member. So it's been an incredibly challenging Tour for him, for sure," Orica Scott DS Matt White told Cyclingnews. "It's pretty hard to quantify that emotional stress."
Chaves himself has suffered more than his fair share of setbacks, most notably that injury he suffered at the 2013 Trofeo Laigueglia that threatened to end his career before it had even begun. Orica-Scott's press officer has urged against asking questions relating to Casas, but while it's not difficult to imagine the emotional turmoil, what shines through – as always – when speaking to Chaves is his remarkable sense of perspective on life.
"At the end of the day, it's just one bicycle race," Chaves says of this Tour de France, and not being able to the level of which he’s clearly capable.
"You can't be mad, and you can't be crazy because you're not climbing with the best, or whatever. You do everything you can do. I trained hard, I went to altitude and I spent time far away from my family. The result is this, and I can't complain.
"I've done six Grand Tours, and I've done three good and three bad, so this is the average, no? It's hard because sometimes people just remember the last good moments, you know? No one remembers my first Vuelta, or my first Giro. You remember last year's Vuelta and Giro, and that's it, but this is life, and sometimes things are really good, like last year's Giro or Vuelta, and sometimes it's hard, like this Tour de France or my first Giro d'Italia."
The important thing, he says, is to enjoy the experience and, in spite of everything, he seems to be doing just that.
"Just to start the Tour de France is special," he said. "Only 200 people each year can be in the Tour de France and this year is my turn. It's cool. It's different to the Giro, the Vuelta or any other race. Everyone tells you that but only when you experience it for yourself can you feel how different it is. I imagine it will be very special to arrive on the Champs Elysées."
After soaking it all up in Paris tonight, Chaves will enjoy some rest before setting his sights on the Vuelta a España. At times it almost didn't make sense to see such a talented Grand Tour rider being dropped on the climbs before some of the sprinters, but the team insist that making it all the way to Paris can only be a good thing.
"It's been good for him to get through to the Tour – it's only going to benefit him for the Vuelta," said White. "He'll take a lot moving forward. Whether he comes back next year, the year after or whenever, he's got this one under the belt.
"Of course he's gone through a lot of emotions over the last three weeks, so to push through and get out the other side, he can take a lot of credit for that."
White has seen enough these past three weeks to be convinced of Chaves' ability to win the Vuelta, but what does Chaves himself make of his prospects?
"If I'm on this level now," he says, "the only way I can go is better."