So will there be a special, out of cycle election to replace Kitzhaber or does Oregon law simply leave in place the next in line? I did not realize OR was one of a few states that does not have a Lt. Governor position... not that that would have mattered much, in all likelihood, in the context of gun laws.
Per the Oregon Constitution, she takes over for him. She will serve just under 2 years until the next general election in 2016, at which she can run to serve the remaining 2 years of Kitzhaber's 4-year term. In 2018, she can then run again for a full 4-year term.