It would be nice if we could get some more libertarian minded Republicans in the Senate who aren't beholden to religious special interests.
Well, I don't believe we've had libertarians in the Senate for quite a while.
As for the original question, this could only really happen in a small state, meaning that this shoudn't happen in TX, MN, MI, IL, VA, NC, GA, NJ, or MA. Also, some of the remaining states will be a safe hold for the incumbent, such as ID, WY, MT, KS, OK, IA, TN, MS, AL, SC, WV, DE, and RI.
That leaves AK, OR, NE, SD, CO, NM, AR, NH, or ME. Or course, it's pretty obvious that SD, CO, NM, and AR won't elect an independent anytime soon, leaving AK, OR, NE, NH, or ME to be the one.