The hat is located at the beginning of Chapter 2 - Anomalous Materials, to the left of the gate which the first Barney you encounter opens for you. However, since getting it requires you having the HEV suit (you need the ability to sprint in order to jump to it), you will only be able to get it during Chapter 3 - Unforeseen Consequences. Instead of going right, through the vent, go back to where you exited the train.
You need to get the hat to xen - jump into the lamba core teleporter with it
I highly recommend saving as often as possible to avoid randomly losing it amidst all the action.