I've just started learning a new piece from the Piano Handbook, (p78 for anyone who has it).

The first bar of 1/8 notes (starting with middle C) is C, G, B, G, A, G, B, G.

I have no problem playing this an octave lower, however when I play it from middle C, I find my left hand tenses too much due to the way it's oriented with the piano. The only way I can play without tension is to move my chair further to the right.

How would you handle this measure?

Gary,
I'm not familiar with the piece, but I do understand what the issue is here. Whenever your hands have to cross in front of the body, it creates an odd angle in the wrist as you try to maintain being perpendicular to the keys. To avoid this, you must first be sure you are sitting far enough from the piano. This will greatly reduce the odd angle as you are better able to move you entire arm to keep the wrist at 90 degrees horizontally to the keys. Secondly, you must lean to the right when your LH gets higher so that you are not crossing in front of the body. Be sure your feet are both planted firmly (calves perpendicular to the floor and not at an angle except when pedaling) and then tilt to the right on your sitting bones.

Whenever the music allows, you can actually play with the wrist being straight in line with the arm. This will mean that your thumb will not be on the keys, so it depends on the music and whether or not you need your thumb at that point. Hopefully this makes sense, but let me see if I can explain a bit better. If you just take your left arm as it is right now and reach across your body to something on your right side, you see that you naturally keep a straight line from elbow to finger 5 (pinky). This is a good angle to play at whenever possible on the keys.

Hope this helps!