I run without a chain tensioner, best thing I ever did for my bike was toss that thing aside... You can't get away with this on EVERY bike, sometimes the chain will rub on stuff depending on the shape of the frame, but if you can get your chain on from front to back sprocket without rubbing anywhere it may be worth a try.
Some will tell you that you need the tensioner to adjust when the chain gets slack, if you run a cheap kit chain this may be true, but I weigh over 200lb and haven't had my #41 chain go slack after almost 2000 miles. This industrial chain can stand up to the job without wearing enough to effect the tension.
When I first built my bike I spent more time messing with that tensioner and broken (kit) chain than I did riding! Finally I got fed up and bought industrial #41 chain and removed the tensioner and haven't had to touch it since, best $10 bucks I ever spent (which got me enough chain for 2 bikes). With the tensioner gone and the #41 chain in place the chain noise is much less, and the resistance when pedaling is WAY less also. Now I can pedal the bike again without feeling so much drag from the motor and don't have to listen to my motor chain making a bunch of mechanical noise as a pedal, it was a big improvement on my bike...