Can the belt drive on a Trek 1st District be replaced with a chain drive?
I have not worked on one of these bikes so I've gone online to find documentation around what parts are on that bike and what might be compatible in chain drive parts.

I think that bike comes with a Shimano 9 spline freehub. If this is true you should be able to:


Replace the chain ring  
Replace the rear sprocket   
Get a chain to match  


and you'll be chain drive. 

Let your local bike shop take a look at it. They should be able to give you a free estimate on what parts and labor will cost and verify the freehub type. Even if you will do the work I always like to know how much I'm saving.

Given your previous issues with the lock ring it would be good to have that looked at. No sense spending the money to go chain if the lock ring isn't going to tighten.

If the local bike shop confirms that they can get a chain drive sprocket for your freehub and a chain ring that will mount on your current crank here are some things to be aware of.

Gearing
If this is your bike then it has a 22 tooth rear sprocket and a 55 tooth chain ring which is a ratio of 2.5. If you like your current gear ratio you will need to go with the exact same size sprocket and chain ring

If you don't like your current gear ratio you'll need to decide what ratio you would like and select the sprocket and chain ring you need.

Chain Alignment
You want the chain to be as straight as possible. 

You can mount the chain ring 2 to 4 different ways - depending on the chain ring type. If the chain ring is flat it can be on the inside or the outside of the crank spider (the five arms that hold the chain ring). If the chain ring is not flat you can flip it over and get different alignments.

On the rear sprocket you can use the spacers to get different alignments.