Joined: Jan 2010
Posts: 9,813
Likes: 1,790
From: Northern California
Bikes: Cheltenham-Pedersen racer, Boulder F/S Paris-Roubaix, Varsity racer, '52 Christophe, '62 Continental, '92 Merckx, '75 Limongi, '76 Presto, '72 Gitane SC, '71 Schwinn SS, etc.
JimP is right about getting the chain length correct.
If you compare length to the old chain, note that it may have stretched, and it's the # of links and not the measured length that is more important in that case.
Those Bell/TaYa "Speedy" (WalMart, Drugstore) chains are the only correctly-installed modern chain that I have seen break under moderate use. Low quality here.
Rusty chains also are very likely to break at the worst time, as they are seriously weakened by weathering!
KMC sells what I believe is the best "very low cost" chain for 7-8 speed freewheels, the Z-model.
A shimano HG70 is much better yet, but costs about $10 more. It will easily outlast the cheap chains but requires somewhat careful installation using only the enclosed "special pin".
You could also install the HG70 chain using a ~$3 KMC Missing Link (NOT the Missing Link II for narrower chain!!!).