I bought a half horse sears garage door opener but there is a beam in my garage running at right angles to the track and hanging down about eight inches. If the opener track was about six inches shorter it would clear the beam. Can the track and chain be shortened a bit?

Yes you could probably shorten them, but if you do, the door probably won't open all the way

Altering the length of the track will do many things and only one good for you. Shorten the track and you must precisely shorten the chain, belt or cable, exactly. Also as stated the door will stop that much shorter than it would have. Tell us how low the beam drops into the room in comparison to the top level of the door when it is opening.