Major 1999 Chrysler LHS Problem

After driving the car approximately 200 miles on the Interstate, the
engine will suddenly shutdown as if it were not getting any gas. The
engine will not start immediately, but after a 30 minute cool down it
will restart and be good for another 100 to 200 miles, until the
problem occurs again. This has occured several times.

The problem has never occured during city driving and there is no
trouble code in the computer.

Any help would be much appreciated.