What city are you in?
Thank you for asking about pet alligators in Oregon on Just Answer.
There currently are no state laws restricting pet alligators and you are not required to have a Class III license to own them. There also is no registration requirements if you are purchasing them in the state and they are found for sale there. Oregon does not regulate them since they can not survive very well in the wild there.
If you are bringing them in from another state, you do have to have proof they are healthy and you would contact the Department of Agriculture for the State to process that. Their number if you need it is(NNN) NNN-NNNN
You would need to check city ordinance with local government and also deed restrictions for the community you reside in to make sure they do not have individual restrictions.
Please let me know if you need any further information on this subject