My citizen folding 3 speed (gear change in hub). Slips as I pedal it. It appears the worst in gear 1. It does not do it with every revolution, but it slips frequently. How do I fix this problem?
Does the chain make a ratcheting sound when you "slip" or is the sound coming from the hub?
My best guess if it isn't the chain is that either the ratcheting pawls in the hub are worn or some of the planetary gears in the internally geared hub are worn or maladjusted.
The first thing you should do is check chain tension. If that's good, then I'd take it to your bike shop. They can quickly:
Diagnose if the shifter is shifting properly and make sure you're not between gears when it's slipping.
Make sure the rear freewheel is working properly.
Check the internal geared hub.
The first problem is super cheap - a simple adjustment. The second and third are more expensive, especially if the hub needs an overhaul or replacement.
1) The chain tension has become too loose. See this Park Tool video for checking proper chain tension, and how to adjust it.
2) The rear sprocket, or chainring (or both) are worn out. See answers to this question for diagnosing if you rear sprocket is worn out: How to tell when to replace cassette?. If the sprocket or chainring are worn and need to be replaced, the chain must be replaced also.