MySQLdb + SSH Tunnel

[Riley Crane]

OVERVIEW:
I am running a script on one machine that connects to a MySQL database
on another machine that is outside of our university's domain.
According to the administrator, network policies do not allow the
compute nodes to access machines outside of our university's domain.

COMPUTERS:
A = compute node within university (I do not have shell access)
B = 2nd machine within university that does not block outside
connections (I have root access)
C = machine outside of university (I have root access)
mysqldb on A cannot connect to C ....but.....
mysqldb on A can connect to B

WHAT I WOULD LIKE TO DO:
Is it possible to set something up where A talks to a port on B, and
that port is actually nothing more than 3306 on C?  Can I do this with
an SSH tunnel?

Can anyone please give precise instructions?