Having the chainring off center will cause the chain to tighten and slack as you pedal. So either the chain gets too tight, damaging itself and other parts. Or the chain gets too loose, possibly slipping and also causing damage.
The passed, missed, and now immortal online Sheldon Brown provides a technique for centering a chainring.
One of the truly great hacks of bicycle tuning, a simple little thing that makes a big difference, as much art and practice as technique, it takes a good feel, steady hands, and patience (the secret weapons of a good mechanic).
Don’t attempt this if you get easily frustrated.
If you’re going to do this, first make sure you have a good chain line. Sight from the back of the bike along the top of the chain, look for a straight line parallel to the center line of the frame and the wheels. You might need to move the chainring from one side of the crank spider to the other. You might need to add spacers between the chainring and the spider. You might need a shorter bottom bracket spindle. You might need to change the position of the cog. You might need to space the rear axle.
A few tricks Sheldon doesn’t tell you:
Loosening the chainring bolts and getting them just finger tight isn’t that hard. Use a good hex wrench. Always follow a pattern as you would with lug nuts, skip two always going in the same direction. (I usually start opposite the crank arm and go clockwise.) Break the tightness of the bolts. Loosen them. Then tighten them just to the point you would have to make the slightest effort to tighten them further. (It’s a feel thing.)
Turning the cranks backwards works much better than going forward. Pedal with your right hand. Have a soft head mallet in your left hand. When you feel the chain tighten, strike the top of the chain behind the chainring. Then pedal back some more and strike when you reach the next tight spot. The hardness of the hit is proportionate to the tightness of the chain. As you get the chainring closer to center, you use softer hits.
Once you’ve got the chainring centered, or as close as it will get, first snug, then tighten the bolts, following the pattern. A chainring nut wrench helps. Then reset the rear wheel.
It takes practice and an understanding of the mechanics involved, but isn’t hard to master.
And it makes a really big difference. I check the chain tension on all single speed and fixie bikes and offer the service to every customer that needs it. Your bike will ride much smoother.