Fix OpenSSL, and everyone that currently uses OpenSSL benefits. Create a new library that's clearly better than OpenSSL, and ten years later there will still be important things that still haven't switched.

I would say that Joel Spolsky answers this quite well:

http://www.joelonsoftware.com/articles/fog0000000069.html

What would be interesting to see is a fork of OpenSSL with the intention of cleaning up the code, removing abstractions where they are unnecessary and adding them where they are, and adding a comprehensive test suite to ensure correct behaviour wherever possible.

Google has already written and released a complete crypto stack for Go. Where you restricting your comments to C/C++ implementations?

The last time I looked at it the go stack was very weak compared to any of the mature C SSL stacks. IIRC it only took me a few minutes to find a security bug (which I reported and is now fixed) that I'd reported against various browsers several years earlier. In short, I highly doubt the go SSL stack is production ready.

The above questioner didn't ask whether it was any good, only whether Google could write and release one.

Good point. Though it only claims to "partially implement TLS 1.2". http://golang.org/pkg/crypto/tls/

The real question is, how hard can it be to do that while starting with OpenSSL compared to starting from scratch?