Any ideas on this chair's history?  

They look like the normal color for new teak, which is essentially what you have there since you sanded away the patina of wood cells on top that had darkened with age. Eventually the wood will turn dark again. (Unless that oil is heavily pigmented---I have never used it.)
They look very nice, if a little newish! I guess now you'll have to sand the 2-seater to match?

I assume it's going to be the same story although this time around I'm going to really try to get it stripped first. I don't mind sanding it if the majority of the brown lacquer is gone but to be honest if I had to sand the entire thing like these it would cost so much money she'd probably not do it. I went way over my estimated time on this job so I don't plan on doing it again. 🙂

The color now looks like about the right color for teak. If you want a lighter brown color, you could have used a different oil. For example Formby's Tung Oil Finish will result in a much more light brown teak color.
Also, the chairs looked To be sun bleached. This lightens the wood a lot to a light yellow color. So when you sanded you took off the sun bleached wood, so it was going to be darker regardless.
And it was possible that there was some water damage too. This causes the wood to go light grey and fuzzy when it is severe. (Although for some oudoor teak furniture this is the preferred appearance). So again this came off with sanding.
Still you would have gotten a lighter brown color with a different oil as an initial coat.
If you redo the matching 3 seater you shoukd do it exactly like these two, otherwise it won't match in the end. Restoring seating is often a lot of work.
Nice job, though. They look great.

Thank you for the compliment and for the suggestion on the Tung Oil, I'll definitely look for it as I have a few personal projects that I'm doing and it's a great chance to experiment.
I wouldn't be surprised if those chairs sat somewhere for a long time where they got sun, since the seat backs were like a tray of over-cooked brownies.
I really loved working on the project and seeing the wood transform. We'll see if she really wants the sofa done... it'll be hard to say no since it's such a lovely set. I guess since I took the sanding route it might even be unfair of me to say no since she'll have a hard time getting someone else to do it the same way that I did. 🙂

Just to be clear, I don't actually like the color of Formby's Tung Oil as an initial coat. I prefer to use it over a Teak oil. I find this best restores the darker streaks and orange colors in the teak. I base this on a Møller table I once owned that had had the cover put on it religiously for its entire life.
Also, some teak is natural very, very dark. My Johannes Aasbjerg pieces are a very dark oily teak. Some other teak is much lighter. Especially plantation grown teak. (And I don't mean the white teak sapwood, the heartwood is just much lighter.)
My teak in my Aasbjerg pieces is in fact so oily that when the raw sanded wood sits for a couple of hours, it develops natural oil spots on the surface. If it is in the sun the oil comes out even faster.

You seem like a real connoisseur of teak - it's fantastic.
Even on this chair there were pieces that retained almost a blondish color and others that were really dark. I should look into learning more about teak. It's very popular and very diverse. I don't think you can handle each the same way (which is clear in how you described your pieces) so I should get my knowledge up in that department!