I have aplication in java and cxf which connects to WebServices with client certificate.
I got certificates form WebService owner
If you are working in Windows OS, you can install the certificate as usual through the IIS, then open mmc.exe -> File -> Add / Remove Snap In -> Double click on "Certificates" Select "Computer Account", next, finish, OK.
Expand certificates, if needed add the certificates from the CA into "Intermediate Certification Authorities" or "Trusted Root Certification Authorities".
Then go to "Web Hosting", here must be your webSite certificates, select the certificate, left click on it, select Export and follow the wizard, the important things to check are "Include Private Key", Include all certificates on the chain, export all extended properties, you must set a password, select the output flie name and this is it. Now you have a certificate with the complete chain on it. No more problems with Facebook or similar.