I did get a successful connection after setting CURLOPT_SSL_VERIFYPEER to false, but I have a hunch that updating curl's certificates might be the proper fix.
So I set CURLOPT_VERBOSE => true and first tried CURLOPT_SSL_VERIFYPEER => true:
* About to connect() to www.google.com port 443 (#0)
* Trying 74.125.67.103... * connected
* Connected to www.google.com (74.125.67.103) port 443 (#0)
* SSL certificate problem, verify that the CA cert is OK. Details:
error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed
* Closing connection #0
And then I tried CURLOPT_SSL_VERIFYPEER => false
* About to connect() to www.google.com port 443 (#0)
* Trying 74.125.67.103... * connected
* Connected to www.google.com (74.125.67.103) port 443 (#0)
* SSL connection using RC4-SHA
* Server certificate:
[…]
* SSL certificate verify result: unable to get local issuer certificate (20), continuing anyway.