It does appear at first glance that it may be gout The right leg looks very swollen, too, though I can't see very much of it. If this hen has genetic kidney problems, it might account for this showing up in one so young. If it is gout and it's genetic, there isn't much you can do about it.
If it's gout from dietary excesses or from excessive use of antibiotics or electrolytes, you can try to increase her water consumption to try to flush the urate crystals. Besides water, offer plenty of "treats" that are high in water content such as raw carrots, raw squash, and melons.
If it's gout, it's painful. That's another way to diagnose it. If she prefers to sit and preen all day instead of ranging and scratching in the dirt, and if she pecks at her feet or holds one up under her belly and then the other, it means she's experiencing pain. Aspirin may help alleviate some of the pain.
It may not be gout, though. There's viral arthritis, and infection that could be behind this swelling. It's impossible to diagnose from a photo, though. An avian vet would be advisable if you have access to one and have the financial means.