Side-to-side chain play

[abacall]

I was cleaning and lubing the chain a few days ago. It was nasty out so instead of going for a ride to warm up the chain, I put the bike on the center stand and put it in gear. For safety I sat on the bike, pushing on the handlebars, front brake pressed firmly, clutch in hand.
When I was looking at the chain I noticed it had some side-to-side play while it was moving. Actually a scary amount of movement. Turned off the bike, checked for tension and it has the right amount vertical movement, but also has a bit of horizontal movement. Is this a sign the chain is on it's way out, or is it normal?
I never noticed this before, but I also never checked.

 

[RJ2112]

Gotta qualify this by saying I've not put my bike on the centerstand to check....

If there's enough side to side motion to notice.... I can't think that's entirely normal. I'd take a good look at the front sprocket, to make sure it's attached properly. If your back sprocket is mis-aligned, the sprocket teeth will run on one side or the other of the space on the roller.... if it's all set correctly, the chain will 'wander' over the rollers to a degree.

As the pins and plates wear against each other, there will be some slop that develops and allows some side to side flexing.