Hopes for a lasting peace settlement in Afghanistan between the U.S.-backed government in Kabul and the insurgent Taliban appear to be at their highest point in years. U.S. and Taliban officials meeting for a fourth round of talks in Qatar that lasted most of last week both reported significant progress on a draft accord that includes a proposal for a U.S. troop withdrawal and a Taliban cease-fire, sticking points that have derailed previous efforts to negotiate a peaceful solution to the yearslong conflict in the country. Zalmay Khalilzad, the Afghan-born diplomat leading the U.S. negotiating team, traveled to Kabul this week to discuss the mechanics of the tentative agreement with Ashraf Ghani, president of the U.S.-backed Afghan unity government, which has been left out of the talks thus far. Despite the progress of the talks, Khalilzad emphasized that the parties have yet to reach an accord and would not finalize a...