Even if the timeline did work out for having chiefdom as an item on a CV, chief residency has a value approaching zero in terms of applying for fellowships and jobs (academic OR community practice). In fact, your phone number on the CV header is probably more important. Quality of CV items, not just quantity, is what counts.
Everyone has to do administrative stuff sooner or later; being chief doesn't necessarily prove that the particular individual is any better at it.
There are plenty of committees a pathology resident could sit on that would offer much more networking and educational opportunities (as well as help get that cherished fellowship), with a fraction of the scut that goes with a chief position. (See the College of American Pathologists website, for starters. Lobbying at a national level gives big-picture insight, as opposed to the narrow scope of a single residency program.)
Unless you are at an institution where:
(1) faculty are receptive to change, and
(2) you cannot say no to your top-shelf faculty because it would hurt your prospects (for internal fellowships or job recommendations), my unorthodox opinion as a senior resident is to avoid being chief.
Disclaimer: I do (honestly!) have great respect for the people who volunteer their time and energy to be chief residents ("someone has to do it"). I just feel like the motivations ("looks good on your CV", "gets you a fellowship" etc.) are not well thought out/based in reality. I don't know where the Myth of Apparent Chief Glory originates. Also, I do strongly feel that rather than throwing residents at every single problem, with adequate dedicated secretarial/support staff, a great deal of nonsensical chief duties could be cut out (e.g. clearing a conference room of leftover food after conference, setting up AV equipment for conference, scheduling talks, designing promotional pamphlets/posters, forwarding "job/fellowship opportunities" email notifications).
I cannot say this enough: For those who are not MD/PhDs and are looking to make the jump from okay residency to top-tier fellowship, timing, networking and publishing are the keys to getting an external fellowship.
Probably in that order.
