If you happen to wander upon the town of Nipton, a man will approach you and happily inform you that he has won the lottery. If you continue to make your way through the rubble, you will find that the Powder gangers who once took this town have now suffered the fate of crucifixion. As you move further toward the town center you will notice Caesar's Legion members near the double doors of the town hall. When you approach, the highest ranked member, Vulpes Inculta, comes toward you and engages you in conversation. He tells you that he will "not have you lashed to a cross like the rest of the degenerates." He wants you to memorize what you've seen in the town, then travel to the Mojave Outpost and let "the Profligates" know "the little sermon" he prepared here. You can continue the conversation and earn some legion fame for telling Inculta that you agree with their methods but he eventually waves you away to teach what you've learned.
Travel west to the highway intersection, then southwest, following the highway up the hill to Mojave Outpost. Two large statues of Rangers shaking hands can be seen from a good distance. Sgt. Kilborn walks around outside and occasionally paths past the statues out of range of the rest of the outpost. When speaking to him, you may either inform him of Nipton's destruction or you may choose to shout a Legion battle-cry and attack him. Either choice completes the quest, resulting in 150XP. No reputation is gained or lost either way.
Note: Selecting the attack choice in the dialogue may turn the rest of the outpost hostile if Kilborn is not far enough away from them. As long as he is near or past the Ranger statues, it should be safe to kill him. Also worth noting, if you select the attack option while wearing NCR faction armor, Kilborn will not attack you and the quest will complete normally.