You can try to export the root of the certificate chain, then import it into your trusted root certificate authority, then check the effect.
The export steps are as follows:
1. Click the lock sign when you access the above site in your browser, Click on the View Certificate link in the right Actions pane.
2. When the Certificate details dialog appears, click on the Certification Path tab.
3. Click on the top-most certificate in the hierarchy in the certification path window.
4. Click on the View Certificate button.
5. Click on the Details tab.
6. Click on the Copy to File… button. This starts the Certificate Export Wizard.
7. Click Next to get started.
8. Use the default DER format and click Next to continue.
9. Pick a location and name to save the exported file as; for example ADFSRoot.cer and then click the Next button.
10. Click the Finish button to export the certificate and then close the wizard when done.
11. Close the other open certificate dialog boxes.
12. Copy the certificate to a SharePoint server so you can import this certificate into your trusted root certificate authority.
13. Run the following useful Powershell to add the certificate:
$cert = Get-PfxCertificate C:\Users\administrator.SE\Desktop\PressReleases.cer
New-SPTrustedRootAuthority -Name "IDDev2010-01" -Certificate $cert