The "speeds" a chain is concerned with is based only on the number of rear casette cogs so you need a 7-speed chain and usually you will find them labeled as 7/8-speed or 8-speed which are the same width. A 9-speed chain (9 casette cogs) is narrower and a 10-speed (10 cogs) is narrower still.

BTW, you have a "21-speed" bike. The number of total gears is calculated by multiplying the number of chainrings by the number of cogs, not by adding them.