I was heading to work, got about a third of the way there, when I noticed my chain was either slipping or skipping. It seemed as if it would engage only every other stroke. I thought this was odd given that when I started riding, it was fine and the problem didn't appear until about 5 minutes in.

I can't see anything obviously wrong. My first thought was that the tensioner arm wasn't engaging so that the chain was too slack to properly engage while pedaling. It looked at a bit of a shallow angle compared to my wife's Brompton when I got home. However, I can't be sure.

I had the bike tuned up about a month ago at what I considered the best bike shop in town, and since then, I've ridden it a number of times without incident.

Any idea what's going on? I'm hoping it's not the IGH itself...

Try tightening the adjustment for the IGH cable a bit.
How old/many miles on your chain and rear sprocket(s)?

Adjusting the IGH occurred to me too. I'll give it a try, although I recall when I changed the back wheel once and I had to adjust the IGH it felt more as if it just would change too easily or not at all, as opposed to the skipping/slippage.

The Brompton is about 3 years old, and I'd say... maybe a 1000 km? I use it semi-regularly, but the distances tend to be less than 10 km.

The IGH cable stretches over time; it's possible that if the cable is too slack for
the IGH to go in and out position/gear. Since this doesn't cost anything; I'd try
this first.

Do you have a chain wear measuring tool? Or maybe ask a shop to do it, there
should be no charge.

Edit: Your mileage is not a lot, but how often you ride in the rain and/or snow
slush will have an affect on wear.

Sounds exactly like a stiff chain link to me. Look at it while spinning back the cranks. You should see something jogging the tensioner.

If it is that, try to loosen the stiff joint by grabbing the chain firmly in the hands either side of the stiff joint, and flexing the chain to and fro perpendicular to the normal direction,the stiff joint under the thumbs.

You mastered the 'put it in second and adjust the cable so the shoulder of the rod that goes in to the axle is even with the end of the axle, indication'. Yet?

Its Aka 'the indicator chain' because of that. may be needed after that wheel change.. you did have to unscrew the cable, to get the wheel Out.

BITD we used the upper portion of the chain tool to gently spread out the side plates of stiff links .. it was safer when the pins were longer than the chain was wide.

Yes, it's been through some mud, dirt, and other gunk. I don't ride many miles, but when I do ride it, I push it pretty hard, especially if I've taken it on trip.

A colleague of mine at work who's a lot more knowledgeable than me said the same thing. I'm going to take a look when I get home.

I've done this before... don't know if I've "mastered it" per se. But I'll have a look tonight.

Problem solved!

Embarrassingly, a twig had wrapped around the rear cog. It had done so tightly that I couldn't tell what it was at first. Part of it had embedded between the teeth so the chain would not engage.

Removed it, cleaned up the gears, and it works great now!

Now I am embarrassed. Exactly the same has happened to me, but I forgot.