Spin the cranks and see if there is any side wobble, the crank may be loose or not seated all the way in. A poor chainline coupled with a crooked crank could cause this, I'd imagine. An oval chainring will definitely cause this. Are you using a crankset meant for multispeed bikes??? They have ramped and/or irregular teeth. Some are shorter than others. This could possibility be the issue. Ask the big brains in the Bike Mechanic forum.

If none of these solves your problems. Sounds like a half-link is what the doctor would order to get better tension.