Chrome 41 ERR_SSL_VERSION_OR_CIPHER_MISMATCH Tomcat 7

I doubt its an SSL/TLS protocol version problem. Most of the time this error means the server and client couldn't agree on which cipher to use. Take a look at this blog post: https://blog.eveoh.nl/2014/02/tls-ssl-ciphers-pfs-tomcat/ on how to enable a secure and compatible cipher suite in Tomcat.

I had the same problem with my Java EE web application running with a self signed certificate on Wildfly 8.1.

You are probably using a 1024 bit DSA public key with your selfsigned certificate and Chrome stops/stopped supporting DSA(DSS).

Creating a RSA 2048 certificate and using it with your web application should solve your problem.