Chalmers joined the RAN in 1958 and chose to specialise in navigation. He served in and during the Indonesia–Malaysia confrontation in the mid-1960s and went on to command from 1981 to 1983. He was awarded the National Medal in 1977. In 1988, he attended the Royal College of Defence Studies in the United Kingdom. He was appointed as an Officer of the Order of Australia in 1992 in recognition of his services as Commander of the first Royal Australian Navy Task Group during the Gulf War. He was appointed Maritime Commander Australia in December 1993, Assistant Chief of Defence Force responsible for Australian Defence Force development and international defence relationships in April 1995, and finally Chief of Navy in July 1997. He was awarded the Legion of Merit by the United States Government in 1998 and retired in July 1999.