Cracked chainstay weld -- now what?

Get in touch with Surly even if it out of warranty. The worst they can do is say no, and even if they won't fix it, they should be able to offer advise on the the best way to proceed. They live or die based on peoples perception of the brand, so have a vested interest in helping you resolve this kind of problem.

Any competent engineering shop should be able to make a reliable repair on Cromo. frames.

You have a few options.

1. Weld it back. Consider this option if you are really tight on budget as the frame would not be as strong as it was before.
2. Contact your bike company. In this case is Surly, they should replace the frame for you if its under warranty. If they do not, then you have to consider options 1 or 3.
3. Get a new frame. This is a tough choice as it would mean spending lots of money. You are lucky if your current bike's components can fit the new frame you are intending to buy.

Just getting it welded by a non-framebuilder could have a couple caveats:

1. I think most framebuilders would approach this in a way where they get full access to the broken face of the dropout, so they could work it down smooth, and then replace either all or part of the chainstay, the goal being to re-do the miter between the chainstay and the dropout to get as much contact area as possible, for as much strength as possible. There are possibly some ways a framebuilder could come up with to make it stronger than new as well. (Another approach could be to put in new dropouts completely, to try and accomplish the same things.) I think it's pretty safe to say that unless it was a defect that got you here to begin with, just going in and re-welding it probably won't make it as strong as new.

2. The frame alignment could get a little screwed up.

3. Non-bike welders have a tendency to not be prepared for just how thin walled bike tubing is. The dropout end of the chainstay actually is just about the thickest walled tube on a bike, so this effect might be minimized here, but the risk is that they blow through it or just do a bad job on the weld because of it, and the flip side is that dropout is very heavy too. (Generally speaking, one of the challenges of bike frames is managing your heat control when you're joining a thin-walled, low-mass thing to a heavy, slabby thing like a burly dropout or a bottom bracket.)

What I would do if Surly doesn't offer anything is send this pic to the nearest reputable framebuilder who does TIG steel mountain bikes, and ask what they think.

A side note is that one of the big questions here is what the dropout alignment was like during the life of the bike so far. Poor dropout alignment often causes failure in this area, as the materials are dealing with a permanent stress from the QR or axle nut forcing them parallel, and the stresses of being a right chainstay are added on top of that. It's sometimes the dropout itself that fails in these cases, but the one in question here is on the strong and totally inflexible side, so the joint would bear the brunt of it.

for what it's worth, I've gone through 4 Surly Troll/Ogre frames over the last four years, all four have cracked at the chainstay (twice on the drive side, twice on the non-drive side) weld. They just did a new redesign in 2017 on both models and I had high hopes - but the 2017 Troll I got after six months of backordering and then trying to get it warranty replaced by Surly, it lasted 2500 miles before it broke again. I'm not bothering to try to get it replaced again (it seems harder and harder to get it replaced under warranty each time - I'm done with wasting my local bike shop's time trying to get it done). I'm going to have the local bike shop (which also does frame building) blast the surfaces, weld it, braze on a brace around the chainstay and do the other side while they're at it. (I might not be using the terms right, I don't know anything about welding myself.)

I don't know what is going on with their manufacturing, but the chainstay/dropout weld is an incredible weak point on the troll/ogres. I would have never bought a Surly bike if I'd known beforehand, or how much time it would take us to get them warrantied each time we had to do it. I've given up on them, even though the design of the bikes is perfect for me.

(and the time the chainstay on my Ogre broke, it was 40 miles from home as the sun was setting and I had to get up & down a 2200 foot mountain to get back home where there was no cell phone service or cars around. I was very displeased with surly on that day in particular. The descent was even harder than the ascent.)

It is a very poor design: the seatstay does not intersect the rear axle but rather strikes the dropout about 2 inches behind the axle. This creates a rotational force on the dropout. The reason it always happens there is that the dropout/chainstay joint on the non-disc side has the most leverage. On the disc side the dropout extends much farther down the chainstay so the leverage is much lower. While there is leverage on the seatstay/dropout weld, the leverage there is also lower. Junk it. The design is flawed. They moved the seatstays way up to make room for the brake caliper and for looks which I think is dumb.