I've only had one chain break on me...rear chain on a Matchless. It broke on the solid side of the split link (below). I hadn't realized that it had broken until I got home and investigate the occasional nasty noise coming from the back as it sometimes caught a tooth on the rear sprocket.
I spoke to John and Jane at Sprockets Unlimited and they said they always break there as its the weakest point of any chain with a split link. The solid side is always flexing slightly because the other side is not rigid. Makes sense.
'28 Model B (future project), '30 Model F, '31 SF31, '35 4F, '38 VB (abandoned project), '39 4G (current project), '46 VH, '48 KG