I'm actually not too sure about my career outcomes, but chemical engineering is a very important field of engineering now, with many technological breakthroughs and a possible environmental crisis on the horizon.
Traditionally, chemical engineers did what we call "process engineering," the monitoring and set up of "processes" used in the mining, minerals and energy industry. It involves figuring out heat flows, chemical flows, etc. Nowadays, chemical engineers are needed for a much larger variety of fields: renewable energies technology requiring chemical expertise, nanotechnology, biochemical research... the possibilities have been opening up in the past century due to advances of scientific knowledge relevant to chemical engineers.
A management degree will have the most synergy with chemical engineering, as engineering is a team job, and team managers are always needed.
However, if teamwork is not something that you believe needs to be institutionalised into you, then you have the choice of accounting, finance and economics, which can lead to a myriad of jobs that Brendan is better at educating you about.