Nearly all wall-mounted light fixtures require electrical boxes behind them.

You might consider getting a metal pancake box. That's a box that is about 3/4" deep and is circular so it'll fit right behind the fixture, and in many cases can be mounted right to the face of the wallboard without recessing it. Since you've got a stud there you've got a good means of mounting it. Some would argue that the internal dimensions of the box don't satisfy the code's volume requirements but given the ease of installation and the existing conditions I'd say it is a major safety improvement.

There are only two major considerations: One is to make sure that you get a grounding screw. You'll connect your house's ground to the fixture's ground, and you'll wrap the house's ground around this screw. No big deal, easy to do. The other consideration is that you'll need to use a romex connector or a plastic grommet in the round knockout in the back of the box where you pull the wire through. The green screws and grommets are pretty much available at any home center.

The one in this picture has integral romex connectors.

 

That sounds like a plan. Now for mounting it to the stud, the stud currently is not directly behind where the fixture was mounted. It is about 3" off center. Any ideas?

I guess I could cut a 2x4 into smaller pieces and build off the stud? I'd like to do minimal wall damage.

 

If I mount the junction box on the wallboard, the light fixture will stick out a bit.

What if I cut (3) 2x4s around 10" in length, and then cut out a small section so that the jnction box can sit "inside" of the 2x4s so it is flush with them? So the box would now be nestled in the 2x4s...hard to explain in text.

The attached pic might help.

 

If you're having to remove drywall then it just makes sense to use a deeper metal box.

Many/most round-based light fixtures will slip right over a pancake box that is mounted to the surface of the wall. It isn't always necessary to recess it. That's the beauty of them, and that's why they get used quite a bit in bathrooms so they can be perfectly centered over the vanity when the home is nearing completion.

If this is just a regular wall sconce, just use a couple toggle bolts or molly bolts to secure it to the wallboard...Assuming there is some wallboard where the box needs to mount up. No need to tear the wall open to add blocking unless you're hanging something really heavy.

 

Not all fixtures require a box behind them and those strip type vanity lights are usually one of them. If the connections can be installed so they are IN the fixture and the fixture is designed for this purpose you need no box.
A very good example would be fluorescent strip lighting. It might just be easier to get a new fixture that requires no box than trying to install a box.

 

Not all fixtures require boxes as JV said, but the vast majority do. Most incandescent strip lights require them, all wall-mounted sconces do, all ceiling mounted fixtures do. The major exception to the rule is, as stated by JV, flourescents.

 

Thanks to everyone. I'm just going to try to mount a box to the 2x4 and go from there.

Thanks.