Chambers was born in Cattaraugus, New York. He graduated from West Point with the class of 1853 (which also included John Schofield and Philip Sheridan), and was commissioned a second lieutenant. He fought in the Seminole War from 1855, and was promoted to first lieutenant in 1859. In May 1861, shortly after the war started, he was promoted to captain, and performed recruiting duty in Iowa. Promoted to colonel in March 1862, he took command of the 16th Iowa Volunteer Infantry Regiment, leading it at the Battle of Shiloh and the Battle of Iuka, being wounded on both occasions. Returning to duty, he led a brigade in the Vicksburg Campaign. In August 1863, he was appointed brigadier general of volunteers and led a division in the XVII Corps, but his appointment was revoked by the U.S. Senate in April 1864. On December 8, 1868, President Andrew Johnson nominated Chambers for appointment to the brevet grade of brigadier general of volunteers, to rank from March 13, 1865, for the Battle of Champion's Hill, and the U.S. Senate confirmed the appointment on February 16, 1869.