He attended the Glasgow Academy from 1895 to 1902, entering the Navy on 15 September 1903 as a cadet at the Royal Naval College, Dartmouth (HMS Britannia).

From 1915 until the end of the war Chalmers served on the staff of Admiral David Beatty, seeing action at the 1916 battle of Jutland aboard the battlecruiser Lion,[1] and receiving a mention in despatches.

[1] From 22 March 1929 Chalmers was "loaned" to the Royal Australian Navy, taking passage aboard the cruiser HMAS Australia.

From February 1937 he was Director of the Royal Naval College, Greenwich, until January 1939, receiving promotion to rear admiral on his retirement.

[1] After the war he worked for the Marconi Wireless Telegraph Company as Deputy to the Managing Director, and wrote several books of naval biography.