I have a Continuum fixie. I try to tighten the chain and in some areas the chain is nice and tight and when I rotate the pedals in other areas the chain is loose. My question is should I be happy with it being tight in some areas and not in others? Thanks Sheila
A little bit of variation is normal, yes. If the chain is so loose at the loose point that the chain falls off I'd call that a manufacturing or assembly defect and take the bike back to where you bought it and get them to fix it.
In more detail the issue is exactly centering the chainring on the bottom bracket/crank, where normally the chainring is not perfectly round or perfectly centred. You can often tweak this a little by slightly loosening the chainring bolts and using the tiny amount of play between the chainring and spider to get a slightly better fit. Loosen the bolts, rotate the crank to the tightest point, pull on the chain to shift the chainring, repeat. You'll almost certainly not be able to entirely fix the problem, but you will probably be able to reduce it.
Some irregularity is not surprising. Lower-priced components are more prone to this than more expensive ones, but that is not a big problem providing the chain is not so slack as to fall off or climb over the cog's teeth, neither too tight that it binds the drivetrain, even slightly.
From my experience (fixed and motorcycle) there can be three causes of this symptom:
Unevenly worn chain is rare, and might occur if you ride a lot having lubricated only part of it. The non-lubed section will wear out faster. Another possibility would be to have a chain reassembled from different chains, but that would be very exceptional.
For the chainring case, the answer provided by Kohi, also mentioned by Sheldon Brown, is the way to go.
Before doing so, it is important to check if the culprit is not the SPROCKET instead of the chainring. By turning the bike upside down and spinning the rear wheel slowly (beware of your fingers on the drivetrain!), watch if the stretching and slacking frequency matches the crank revolutions or the wheel revolutions. If it matches the wheel's, then the sprocket is off-center and the eccentricity cannot be eliminated. In this case, discover the wheel position that is tighter, and adjust the chain slack in that position.
As a final note, when I first installed my crank, I tried to center the ring by loosening the bolts, just to discover that the ring didn't move at all: it was already precisely "seated" in the spider. If it wasn't perfectly centered, it would not be possible to center it using this method (or at least without filing away some metal). Just to make it clear, it was (and still is) the sprocket that was a bit off-center.
Hope this helps!