single speed chain

You'll be fine using any chain so long as it fits onto both cogs, although a SS specific one may derail less and last longer as well as be slightly tougher
 
It depends on your sprockets. There are two widths that are used; 1/8" is the traditional SS width, and 3/32" which is typically used for multi-gear setups, but is becoming more common on SS due to conversion kits etc. 9-speed chain won't fit on 1/8" sprockets.
 
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