A few years ago I purchased a NIB Nickel 34-1 4". I have only shot a few boxes of 22LR through it. My problem is that the fired cases always stick in the cylinder and I have to tap the hand ejector tip to get them out.
What would be a good solution to this problem?
Well I'm a bit late to this party but I see that you've had all good conscientious posts in response to provide you help.
They range from mild to gold plated.
I always attempt to fix problems with the very least invasive method.
Also I would never tolerate a sixgun that was finicky with certain brands of ammo, especially these days when certain specific brands are so hard to find. Having said that, I do recognize that each gun has its own preference for the best accuracy and I will cater to that.
But the fact is, many chambers come from the factory with less than satisfactory chamber finishes. This is exacerbated on a nickel gun because the plating does add a smidgeon of extra thickness on the metal surfaces and can make chambers a little extra tight.
However in my 59 years of shooting experience I've never had to resort to a gunsmith or any added tools expense to fix chamber extraction issues.
A simple inspection for burrs and polishing is all I've ever needed. And I have more S&W .22s than any other models. Britbike1's method is an excellent first thing to do. Quite often one burr in one chamber make all six extract too hard.
I shoot one round in each chamber and extract that one case to find any chamber or chambers with a specific problem or a burr.
Then I polish all chambers gently. The simplest for me is 800 to 1000 grit paper wrapped around a wood dowel with a slit in it, just slightly smaller than the chamber diameter. Mount in a Dremel tool or small power drill and spin in the chamber. It only takes a coup[le of seconds per chamber.
You can even go up to 2000 grit or, as Tops posted, use Flitz. On an S&W barrel mop, the chambers will look like mirrors!!
One caution is to stay out of the chamber throats, you don't want to affect the shoulder or throat area.
Of course .22s chambers are simplest to do because they don't have actual chambers, they have charge holes, no shoulders, (not .22 Magnum chambers, they have shoulders).
The secret to success is to keep the dowel moving in and out of the chamber so you keep the chamber walls straight. If you don't move the dowel or any polishing device for that matter, in and out, you risk creating waves or wallows in the chamber walls and cases will stick even worse.
But as I said only a couple of seconds is needed so there's little risk of the problem occurring and no risk if you move in and out using a dowel.
The risk is greater using polishing compound on a patch because it doesn't have straight sides. Especially if used with a power tool and not moved in and out.
I'm sure you'll have no problems after that and enjoy that beauty for the rest of your life.