Squire H. Madden, attorney, son of William Madden, was born on October 3, 1860, on the family farm near Knoxville, Tennessee. He had little formal schooling but educated himself and in June 1884 graduated from Carson (later Carson-Newman) College. Shortly afterward he moved to Texas and taught school for a year at Pilot Point before reading law in the office of Alvin C. Owsley at Denton. There he was admitted to the bar on July 22, 1887. Soon afterward, Madden moved west to the new railroad town of Panhandle City in Carson County and opened a law office, which he shared with Orville H. Nelson. A few months later, however, he moved to Clarendon, in Donley County, and formed a partnership with James N. Browning. Appointed attorney of the Thirty-first Judicial District, Madden was among those presiding at the opening session of the first district court at Amarillo in June 1888. In 1891 he represented the Wisner interests in the celebrated lawsuit over ownership of Block 88 in Amarillo (see AMARILLO, TEXAS). In Clarendon he married Orie Hendrix, and they had a son and two daughters.
In January 1894 the Browning and Madden law firm moved its offices to Amarillo. Two years later J. J. Hagerman's Pecos and Northern Texas Railway began construction of its line, which was slated to extend from Roswell, New Mexico, into the Texas Panhandle and connect with the Southern Kansas line at Washburn, in Armstrong County. After learning of that proposition a group of Amarillo citizens led by Henry B. Sanborn sent Madden to Chicago to persuade the Santa Fe railroad officials to reroute the line through Amarillo. The success of that mission ensured Amarillo's future as the "Queen City" of the Panhandle. Madden subsequently became attorney for the Southern Kansas (later Panhandle and Santa Fe) Railway, and during his career Charles Goodnight, Robert B. Masterson, Lee Bivins, and many other prominent area cattlemen were numbered among his clients, as were several corporations, including the Rock Island line (see ROCK ISLAND SYSTEM) after it built through Amarillo in 1902.
In 1906, after Browning became district judge, Madden formed a new partnership with Otis Trulove. Other attorneys who were partners in the firm at one time or another over the next seventeen years were W. H. Kimbrough, F. M. Ryburn, and H. C. Pipkin. By 1924, after Trulove retired, the firm had been reorganized as Madden, Adkins, and Pipkin. Madden was one of the original stockholders of the American State Bank, the Panhandle Pipeline Company, and the Amarillo Gas Company. Over the years members of his family accumulated substantial property and were heavily involved in community affairs, including a tree-planting project in Ellwood Park. In 1923 Madden suffered a nervous breakdown that affected his general health and prompted occasional visits to a sanitarium in San Diego, California. There, on January 7, 1927, he died suddenly from a heart attack. His body was brought back to Amarillo for interment in Llano Cemetery.