My family lives in Beaverton so I had good luck in Washington County Sheriff's office located in Hillsboro. I've heard that many people have had good experiences with Multnomah County also.
Go to one of their websites, download the form and fill it out. When you get to the part about providing good reason, provide anything that applies to your situation. Self defense is good, but if you have business interests in Oregon, or if you have multiple family members in Oregon, or need to travel between maybe more sketchy parts of town late at night, these are all applicable reasons. It probably also doesn't hurt to mention that you take safety very seriously, etc.
Oregon requires that you show up to apply for or change any details on your permit. They also require that you've taken a pistol safety course, such as basic pistol from the NRA and display proof of this course on application.
And don't forget to read up on Oregon's laws regarding CHL, while they're similar to Wasington's, they're not all the same and it would behoove you to know exactly what you can and can't do.