Tarnishing is quite normal!
Most chains are plated; the only types of chain that will not tarnish are gold-fill and sterling silver (silver does tarnish, but it can be easily cleaned off).
The longevity of the chain's quality depends on how the chain is worn and the maintenance of it.
Electroplated chains tarnish rapidly under both hot and humid conditions. Any moisture (e.g. water, sweat) will further the oxidation process.
The chain will tarnish, but depending on how well it is handled, the original quality can last from one day to even a year.
If this is a major concern, please not purchase plated chain/findings, gold-fill and sterling silver chains are a good, but pricier alternative.