How to get server certificate chain then verify it's valid and trusted in Java

The method you want is getServerCertificates, not getServerCertificateChain. There is some nice sample code here.

EDIT

Added some sample code of my own. Good starting point for you. Don't forget to look at the Javadocs for HttpsURLConnection and X509Certificate.

import java.net.URL;
import java.security.cert.Certificate;
import java.security.cert.CertificateExpiredException;
import java.security.cert.X509Certificate;

import javax.net.ssl.HttpsURLConnection;

public class TestSecuredConnection {

    /**
     * @param args
     */
    public static void main(String[] args) {
        TestSecuredConnection tester = new TestSecuredConnection();
        try {
            tester.testConnectionTo("https://www.google.com");
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    public TestSecuredConnection() {
        super();
    }

    public void testConnectionTo(String aURL) throws Exception {
        URL destinationURL = new URL(aURL);
        HttpsURLConnection conn = (HttpsURLConnection) destinationURL
                .openConnection();
        conn.connect();
        Certificate[] certs = conn.getServerCertificates();
        for (Certificate cert : certs) {
            System.out.println("Certificate is: " + cert);
            if(cert instanceof X509Certificate) {
                try {
                    ( (X509Certificate) cert).checkValidity();
                    System.out.println("Certificate is active for current date");
                } catch(CertificateExpiredException cee) {
                    System.out.println("Certificate is expired");
                }
            }
        }
    }
}

Quick googling brought me to this example using BouncyCastle. I think it better answers the question. http://www.nakov.com/blog/2009/12/01/x509-certificate-validation-in-java-build-and-verify-chain-and-verify-clr-with-bouncy-castle/