My tomcat server is fronted by Apache2 and Apache handles SSL negotiation. I discovered that I had improperly installed the intermediate certificate for GoDaddy and while modern browsers just ignored the resulting misconfiguration, Java was complaining.
I had set the SSLCertificateChainFile directive to point to the "cert-chain.crt" file. The mistake is understandable given the near identical naming of the directive and the file...but alas that intuitive connection is erroneous. The directive instead needs to point to the gd_intermediate.crt file that GoDaddy also provides. Here's what my correct config looks like on RHEL5:
SSLCertificateChainFile /etc/pki/tls/certs/gd_intermediate.crt