ORS166.170 (1) Except as expressly authorized by state statute, the authority to regulate in any matter whatsoever the sale, acquisition, transfer, ownership, possession, storage, transportation or use of firearms or any element relating to firearms and components thereof, including ammunition, is vested solely in the Legislative Assembly. (2) Except as expressly authorized by state statute, no county, city or other municipal corporation or district may enact civil or criminal ordinances, including but not limited to zoning ordinances, to regulate, restrict or prohibit the sale, acquisition, transfer, ownership, possession, storage, transportation or use of firearms or any element relating to firearms and components thereof, including ammunition. Ordinances that are contrary to this subsection are void.
HOWEVER, there is also:
ORS166.173 (1) A city or county may adopt ordinances to regulate, restrict or prohibit the possession of loaded firearms in public places as defined in ORS 161.015 (General definitions). (2) Ordinances adopted under subsection (1) of this section do not apply to or affect: (a) A law enforcement officer. (b) A member of the military in the performance of official duty. (c) A person licensed to carry a concealed handgun. ....
It continues with the exemptions, but the important part is there, they CAN regulate possession in public places, unless you have a CHL. Portland courts have defined the interior of your car, and even the deck of your house as "public places" for the purposes of this law.
Portland, Eugene, Beaverton and a few other areas have local ordinances against open carry. In these areas, a CHL is your friend.