* Illinois sues to block Trump’s troop deployment to Chicago * Fourth legal challenge over federal use of National Guard in cities * Courts in Oregon and California say Trump likely overstepped * U.S. says Texas National Guard troops in transit to Chicago (Adds court hearing on Illinois troop deployment paragraph 2) By Nate Raymond and Dietrich Knauth Oct 6 (Reuters) – Illinois launched a legal challenge on Monday to block U.S. President Donald Trump from deploying hundreds of federalized National Guard troops into the streets of Chicago – the latest flashpoint in a growing number of court battles over the Republican president's authority to deploy military forces domestically. U.S. lawyers told the U.S. district judge overseeing the case during a hearing on Monday that the Texas National

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