If you mean a place where your luggage can be locked away so that only you can access it. . . the answer is no. All Amtrak passenger cars have open luggage racks above the seats. Depending on the type of car you're traveling in, some also have open shelves or empty floor space where suitcases can be stored.
The truly paranoid sometimes use a bicycle cable and lock to secure their bags to the rack. But when I travel in coach, I simply place my bags in the overhead rack, keep them locked, and position them so the zipper or latches face the car wall. That makes it much harder for "unauthorized persons" to casually peek inside while passing by.
Petty thefts don't happen often, but they're not unheard of -- especially at night when passengers are asleep. Just use common sense. Don't leave valuables (cell phone, camera, electronic equipment) unattended. Always lock them in your bag -- or take them with you -- when you leave your seat.
It also doesn't hurt to put yourself on a "hello" basis with one or two friendly-looking passengers sitting nearby. That way, in the unlikely event that a stranger takes an interest in your stuff when you're not around, your new pals will be more apt to challenge them.
Have a great trip, and don't forget to look out the window.
[This message has been edited by dilly (edited 12-21-2003).]