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The SSL_set_verify_depth OpenSSL method is not currently exposed by the ssl module. The context object would seem to be the proper place for it as an instance method.

+ if (depth < 0 || depth > 100) {
Why 100 and not 10 or 1000?
SSL_CTX_set_verify_depth() is unable to check the depth?
The patch lacks unit tests and documentation.
The patch is for Python 2.7, it would be better to write a patch for the default branch (future Python 3.6).

I had thought that I had found documentation that the max depth is 100 and anything higher is ignored -- and as I read that back to me, I believe I read an example passage and interpreted it incorrectly. I'll remove that.
We primarily use Python 2.7, so I started there. I'll submit another patch with changes on the 3.5 branch and add tests.

Attached is a patch for the 3.5 branch. The test is minimal -- we are relying on the underlying OpenSSL library and its context to manage the data. I have removed the data validation from the set function -- OpenSSL seems happy to accept negative numbers for depth, even if that is a non-sensical value. I have started on the documentation, and can do a more comprehensive job if the code section is good or mostly good. I'll do the same for the 2.7 patch.

The patch looks fairly simple, but what is your use case? I don't like to clobber the SSLContext with additional features. I have never been in a situation that required me to change the verify depths for chain building. Why do you want to restrict or enlarge the verify depths? OpenSSL's default verify depths is sensible.

+1 on making sure we have a concrete use case before expanding the API

The use case is for an internal PKI implementation where verification should be, needs to be limited to certificates signed by the PKI CA and no higher to, say, a larger realm which would not be appropriate.

Grant,
I'm not sure I follow you. Do I understand correctly that you want to call SSL_CTX_set_verify_depth(ctx, 1), in order to enforce that a peer cert is directly signed by your CA?
That doesn't sound like a good use of SSL_CTX_set_verify_depth(), because it only works for a simple case without an intermediate CA. Most real-world cases have one or more intermediate CAs.

For the use case of "I want to trust this CA, but I don't want to trust any of it's sub CAs" I think there's a simpler solution than expanding our API:
Create your own cross-sign of the root you want, and add a pathLenConstraint: 0 to the basicConstraints extension.
By create a cross-sign, I mean a new certificate with the same subject/SPKI/SKI/other-extensions, but instead of being self-signed, sign it under some random private key you throw away. And then use that as your trust root, instead of the original certificate.
This should work fine for validation.

Both Alex and I agree that verify depth is not the right solution to solve your problem. I'd rather not add more APIs unless they are useful for general audience. OpenSSL has a good default for verify depth.