Chesterman's network of health dispensaries employed preventive medicine using the new drug tryparsamide to combat the prevalent issue of sleeping sickness in the area.

Such success led to his methods being widely adopted in Africa, making Chesterman a prominent contributor to the field of tropical medicine.

He was born into a large Bath family that had a history of strong Christian connections going back to Neuchatel, Switzerland, and to the west country.

His desire to pursue a career in tropical medicine especially stemmed from his responsibility for a malaria diagnostic service under his apprenticeship to Major Philip Bahr in Palestine.

Additionally, he received the Serbian Red Cross medal and was given the position of the Officer of the Order of the British Empire (OBE) in 1919 in recognition of his efforts with malarial patients among the troops in Damascus.

He worked in collaboration with the Belgian authorities and such a partnership allowed for the development of a network of village dispensaries staffed by Congolese auxiliaries.

Rather than relying on the improvement of standards of living and public hygiene, Chesterman advocated for the mass use of chemotherapy, which complements his support for the motto "prevention is better than cure".

He also believed that the development of a programme of simple health posts that functioned through the service of trained and supervised medical auxiliaries would support the adoption of Western medicine in tropical Africa.

This model would be further developed by Stanley George Browne in Nigeria leading to Chesterman's design being implemented to manage infectious diseases across the continent.

In 1938, Chesterman attended the World Council of Churches meeting in Madras, where he persuaded Ida Scudder to allow the admittance of men students to the Vellore Women's Medical College.

However, after the war, he became a renowned consultant in the subject of tropical medicine and was in great demand by the Colonial Office, insurance companies and foreign governments.

Additionally, he published a variety of articles on tropical medicine, as well as In the Service of Suffering, a popular history of medical missions.