Phil Mickelson was playing in Singapore this weekend while Woods found himself trying to catch Chalmers, a far more obscure left-handed golfer, at the Australian Open.
He ultimately came up 2 strokes short, but to Woods, the opponent was really of little concern.
For most of the past two years, the opponent has been himself, as he fought through personal issues, swing changes, injuries and inactivity. A third-place finish at The Lakes Golf Club might not have been the desired result, but it is still Woods' best finish in an official tournament since he won the Australian Masters -- over Chalmers -- two years ago.
"He hit the ball great this week; his iron play was phenomenal,'' said Woods' caddie, Joe LaCava. "I'm pretty pumped about that. Corde Valle [Frys.com Open] he didn't play as well as here. He hit the ball very, very solid. As solid as I've seen the guy hit it.''
LaCava has been on the bag for all of two tournaments, but he's been around long enough to see plenty of Woods' game. He caddied for Fred Couples for some 20 years, then had a brief stint earlier this season with Dustin Johnson.
But when Woods was in search of a caddie after parting ways with Steve Williams earlier this summer, LaCava became intrigued. He left Johnson after the Tour Championship, saying he did so for a simple reason: "Because he's Tiger Woods.''
Clearly LaCava believes that Woods will return to his old, winning ways. Why else would he leave a lucrative bag like the one he gave up with Johnson, who is the fifth-ranked player in the world, just 26, and seemingly with years of great golf ahead?
Like many who are close to Woods, LaCava believes the former world No. 1 has too much talent, too much game, to simply fade away.
"I said to myself, after this week, I thought Fred hit the ball very solid,'' LaCava said. "But this guy he doesn't put Fred to shame, I don't want to knock Fred. They're both phenomenal. I always thought Fred flushed it, but this guy flushes it more than anybody I've ever seen.''
You can't read too much into one tournament, but this was clearly a positive step for Woods, who has struggled to gain any consistency, any momentum, over the past two years.
When was the last time Woods hit 75 percent of his greens in regulation? That's what he did here, hitting 54 of 72 for the week. He hit 12 of 14 fairways on Sunday, a bit misleading because the 6,900-yard course meant few drivers.
And the two fairways he missed proved to be huge, both leading to bogeys. Woods badly missed the 11th fairway, a par-5, leading to a bogey -- his second in two days at that hole. And then he hit a poor drive at the 310-yard, par-4 13th, a hole that playing partner Aaron Baddeley drove on Sunday.
Woods attempted to do the same thing and hit his drive way right and was plugged in a hazard. He barely was able to extract his second shot and made a bogey on a hole that Chalmers birdied. That 2-stroke swing is one of several you could point to over the final two days.
"The plan was to hit driver with that kind of wind, no matter the situation,'' LaCava said afterward.
Woods later second-guessed himself, saying that he should have laid up on the hole. That would have meant a 5-iron off the tee and then a wedge to the green. That is the beauty of a risk-reward short hole such as the 13th.
"I shouldn't have gone for it, now, in hindsight,'' Woods said. "Unfortunately, I made a mistake there.''
Is it one he would have made if Williams were still on the bag? It is something interesting to consider in light of all the recent caddie chatter.
Williams' strength is his conviction. Perhaps he would have been 100 percent behind the decision to hit driver at the 13th. But if he wasn't, he would have said so.
LaCava is in a bit of a different spot. This is just his second tournament (he did spend time with Woods last week in Australia for various clinics and exhibitions) and he is still feeling his way. He wasn't offering his opinion much as he gets comfortable in the new role. All of which is understandable.
"It takes a while, but right now I would say it's pretty good,'' LaCava said of learning to caddie for Woods.
That comfort level will come as Woods plays, and LaCava acknowledges that is the only thing holding him back right now. He is in the midst of playing three tournaments in four weeks, including the Presidents Cup this week at Royal Melbourne.
There, the vibe will be different, the kind of golf required not the same. But it is another opportunity to put his game under duress, something that was inevitable given the controversial nature of Woods' selection to the U.S. team by Couples.
"Everybody's pulling for him,'' LaCava said. "I look over two fairways and nobody's following anybody else. And they're all great players. Which is too bad for the other guys. Of course, everyone's pulling for him. You can even see guys like you [the media] I think wanting him to do well.
"Which is better for the game, don't you think?''
You wouldn't often say that finishing behind Chalmers and John Senden -- two journeymen players who have one victory between them on the PGA Tour -- is a good thing, but Woods could care less about the names who beat him at this point.
He finished as the low American, had three strong days, and was encouraged that he was able to fix the issues in his game from Saturday.
"I pretty much hit it on a string,'' he said.
Bob Harig covers golf for ESPN.com. He can be reached at BobHarig@gmail.com.