I would venture to say (and Blam confirmed with his link to the manual) that you have some excessive slack in that chain, and removing it would help.
In your first picture, where you're holding the chain, it looks like there is a lateral movement available on what appears to be the axle shaft, to the right. I'd loosen those bolts and try to slide the rear axle backwards to tighten up the chain. Since you have a trike, you'll have to move both sides of the axle evenly backwards to keep the wheels parallel to your direction of travel, or you'll end up with the tires scrubbing as you roll forward.
From the scratch marks on the frame, it looks like you may have played with this already, and if the axle is at its furthest rearward setting, you may have to move the intermediate axle (the left one in your two pictures) forward. Of course, doing so will introduce slack in the other chain. Since the other chain is likely connected to the cranks, which won't have any fore-aft adjustment, this may not work for you.
That leaves you with option 3 which would be to remove some links from that intermediate chain (the one you're holding in picture 1), then readjust the rear axle forward to accommodate the now shortened chain. To do this, you'll need a chain tool that will push the link pin out of the chain, then push it back in when you've taken out a couple of links. You can buy one (bring the trike with you, as different chains may need different size tools), borrow one from a friend, or take the trike into a shop which will have a stock of them in their shop. They probably wouldn't charge much to make a small adjustment like this.
After a second look, it looks like the slotted frame that holds the secondary chain is a separate piece that can be pushed backwards to tighten up that chain. Loosen the bolts holding the intermediate axle (on the left), then push that slotted frame backwards to tighten the chain (again, make sure it's even to keep your rear wheels parallel to the direction of travel), then tighten. Confirm this with the link to manual in Blam's answer.