He obtained a Bachelor of Science Degree in Quantity Surveying from the University of South West in the United Kingdom.
He was formerly Deputy Minister of Natural Resources, Energy and Environment, and then served as Justice Minister. Chiume established his own consultancy of Chartered Quantity Surveyors in Lilongwe. Chiume joined the Democratic Progressive Party (DPP) and became the party"s Administrative Secretary.
He was appointed Deputy Minister of Natural Resources and Energy in the cabinet that became effective on 15 June 2009.
He was confirmed as Deputy Minister of Natural Resources, Energy and Environment in the reshuffle announced on 9 August 2010.
He is a member of the Royal Institute of Chartered Surveyors in the United Kingdom, and the Surveyors Institute of Malawi. From 2008 he was a member of the DPP Governing Council. On 19 May 2009, he was elected Member of Parliament for Nkhatabay North Constituency on the DPP ticket.