What size chain is typically used when hanging a porch swing?
A standard double loop chain is often used for porch swings.
Assuming three hefty occupants (~250 lbs each) and a 100 lb swing, you're up to a load of 850 lbs. If you use 4 lengths of chain to connect the swing, that's 212.5 lbs per chain. So you need at least 2/0 chain, which is rated to a working load of 255 lbs and an UTS of 1020 lbs.
EDIT: If you're a nerd/engineer like me, you can get more technical and take into account angle of the chains from vertical and normal acceleration from swinging. Then your equation comes to:
4*T*cos(Θ)-m*g=m*a where a=v^2/(l*cos(Θ))
T is the tension per chain length using a total of 4 chains, m is the total mass of the system, a is normal acceleration, l is the chain length, v is maximum horizontal velocity you'll be reaching, and Θ is the angle of the chains from the vertical
which will be a bit more than 255 lbs if you're swinging very fast, or have very short chains or a very wide swing. In that case, you may want to go with 3/0 chain.