The trouble is, no-one seems to know what variety it is. It was given to me in good faith as "Purple Gusto", but it is evidently not that. "Purple Gusto" has long, pointed fruits, but the fruits on mine are bulbous. Some of them are a light "plum" color like this:
Others are much darker, like this:
Someone suggested this might be "Cheiro Roxa", but I think not, although there is some similarity.
Whatever this is, it's a very attractive chilli! I haven't tried eating any of the fruits yet, so I can't comment on the taste or heat. In fact I will struggle to tell when they are ripe. Perhaps they will turn red or something?
If you recognize this chilli / pepper, please tell me in a comment!