This error occurs when the mysql client cannot open the TCP connection to the remote DB server.
Make sure you are specifying the host and port correctly:
mysql -h -P 3306 -u chris
Try to connect using telnet to check if the port is open and not blocked by a firewall:
telnet 3306
If this works then your MySQL connection details are incorrect (wrong user?)
If this does not work then it is a network problem and not a MySQL problem. Try checking your firewall to make sure that the client machine is permitted access to the MySQL port on the database server.