Can the fan be rewired so the fan works off the pull chain and the lights work off the switch?
The only way to know for sure, is to pull the fixture down and have a look at the wiring. If power comes from the panel to the fixture first, then this is trivial. If power goes to one of the switches first, then you're likely out of luck.

If you are lucky, and the power does go to the fixture first. Simply connect the black wire from the fan, directly to the ungrounded (hot) supply conductor. Leave the blue wire from the fan connected how it is.

As BrownRedHawk mentioned in a comment, installing a remote might suit your needs. Though you may want a remote at each switch location, which complicates the installation a bit.