There are a few parallel parking spaces along the building's entrance drive that runs from MLK Jr Blvd to Multnomah St. If those spots are full, your next best bet would be one of the metered spots along NE 3rd Ave just north of the Union. Not a ton of nearby parking options, so I'd definitely recommend for visitors to take the bus or MAX if possible since there are several stops nearby.
The quickest answer is not really. There are parallel spots near the building, but they are almost always full. Otherwise, there are some metered spots across from Unity Hospital on 3rd Ave.
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