Chopping an old BSA or anything with a bit of value or worth to someone would be a shame. 30 years ago, and more, people were chopping Triumphs, BSAs etc because they were readily available and few people seemed to care.
The British bike industry was dying a slow and painful death but there were firms producing girder forks and stretched frames to take Brit engines and there was quite an industry. Times and tastes change. There are far more people out there producing/selling original and pattern parts to restore these old bikes than to make choppers out of them.
Having ridden a very well constructed Triumph 650 chopper, not mine and some years ago, I would have to say that it looked the part in the shop windows as I passed. If you rode on arrow-straight and smooth roads it was comfortable but show it a bend and it could change your life (not in a good way!).
There is also the whole pseudo renegade crap that goes with the chopper scene that you really don't want to buy into (biting heads off live chickens is so 70's).
If you've got an old BSA, find out what it is, or was, then see how much of the original you have got. You might find a picture of the same model on this site. You can then look into restoration to whatever level you wish or chop it, if you really have to. I would bet good money that the restoration might even be easier to accomplish and certainly more satisfying.
