http://arpnetworks.com/ offers OpenBSD VPS, and has a great service record! I strongly recommend them.
Digital Ocean supports FreeBSD, but not OpenBSD. Which is close, but not quite the same. Perhaps with a little persuasion, they could be talked into it
You can install and run OpenBSD on DO. Here's the guide by Derek Sivers: http://50pop.com/d.html
Thanks! I think I'll give that a try. That's a great idea.
Please do!
It's even possible to do modern web stuff on OpenBSD. Erlang and Elixir run on it, as does Postgres. Phoenix framework pretty much works out of the box.