There sure is. I made an appointment a couple of weeks ago when I was in town on business, but had to cancel due to a conflict.

The place is called "HairM" and it is a specialty men's barber/salon. They have a location in Downtown Portland and another in Beaverton.

http://www.hairmgrooming.com/000260.shtml

Kind of pricey, but they do offer something of a premium service. If I lived in Portland I would certainly consider the King's Club and receive a years worth of haircuts (up to 16.)

They have one specialist, Ratany, in the downtown shop who does straight razor shaves. You have to specifically make an appointment with her.