Remember that chains don't wrap around the pitch circle of sprockets, but instead form a polygon. The difference in circumference of these shapes can change the chain tension as the sprockets rotate (especially with small sprockets), so you always have to leave a bit of slack on the chain (but not too much or you'll jump teeth!).
Also note that the chain will grow with use (as the individual bushings wear). If you have a mounting that doesn't let you adjust tension, you may have to replace chains at some point (no idea how often in an FRC context).
Tsubaki has a good write up on page 15 of their chain guide here:
http://www.ustsubaki.com/pdf/iandm_guide.pdf