CHICAGO, Dec 20 (Reuters) - Chicago Mercantile Exchange lumber futures closed higher on Thursday amid talk that low supplies at lumber yards have forced dealers to pay higher prices to restock, analysts and CME trader said. CME lumber closed up $3.10 to 50 cents with January up the most at $247.00 per thousand board feet and March up $1.00 at $252.80. Saw mills were selling cash lumber at $228.00 per tbf on Thursday, which was up from $220.00 earlier in the week. It was also up from the midweek Random Lengths cash quote of $219.00. "Prices are moving up because there is not a lot of wood in the pipeline," said Neil Schmaedick, forest products analyst with Salomon Smith Barney. Lumber dealers had let inventories run low amid ideas there would be more wood coming in from Canada after a U.S. countervailing duty on Canadian lumber expired. The duty expired on Dec. 15 but the flow of wood from Canada remains light, said Schmaedick.