Montgomery played for the Philadelphia team against New York (1855-1856) and won two postal games. His only major tournament was the First American Congress, a knockout tournament in which draws did not count. The Congress, organized by Daniel Willard Fiske, was held in New York from October 6 to November 10, 1857. The top sixteen American players invited were: William Allison, Samuel Calthrop, Daniel W. Fiske, William J. Fuller, Hiram Kennicott, Hubert Knott, Theodor Lichtenhein, Napoleon Marache, H.P. Montgomery, Alexander B. Meek, Paul Morphy, Louis Paulsen, Frederick Perrin, Benjamin Raphael, Charles H. Stanley and James Thompson. The first prize of $300 was refused by Morphy, but he did accept a silver service consisting of a pitcher, four goblets, and a tray.
In the first round Montgomery defeated William S. Allison by a score of 3 wins to one. In the second round he was knocked out by Louis Paulsen who had scored two wins and was declared the winner when Montgomery had to return to Philadelphia. Three wins were required to win the match.
Montgomery founded the Philadelphia Chess Club and became its first President. In 1859 his win in a correspondence game gave Philadelphia the victory over New York and in 1860 he won the club's first championship. In 1861, Montgomery played a match against New York's Theodore Lichtenhein and lost +2 -7 =1 and as result, he practically retired from serious chess. The only exceptions were a match against James A. Leonard in 1861 whom he defeated by a score of +8 -4 =2 and a match he lost to Gustavus Reichhelm +4 -8 in 1864.
After retiring from chess Montgomery lived in Philadelphia and New York where he practiced law until he moved to Marysville, California. Far away from home and old friends and the scenes of old triumphs and defeats, he was stricken down by a stroke of paralysis at the age of thirty-six.
Montgomery's style was described as one of daring brilliancy. He delighted in giving full sway to his vivid imagination and his combinations were astonishing for their originality and audacity. His style of play was nervous and rapid and his offhand games were always accompanied by a running good natured banter. The weak side of his play was a constitutional defect which no amount of chess knowledge, experience or ability could overcome...he could not endure defeat.