2 solutions:
1) You want to have a different home directory : 1 in the chroot and one in the real /. Then you need to copy Xauthority
Code:
cp /home/user/.Xauthority /chroot/home/user
2) You want to share the same home directory between the chroot and the real /. Then add this to the "real" /etc/fstab (not in the chroot)
Code:
/home /chroot/home none rbind 0
But all the links in /home that points to something in the real / will be broken