(something a little different here - instead of a new character created from scratch, this post details the changes I've made for my own campaigns to the classic organization used in so many V&V games)
Pawns represent about 99% of the overall membership of C.H.E.S.S. Agents of this rank are almost never referred to by said rank (except occasionally when getting dressed down by a superior officer), and any agent not referred to by a higher rank is usually assumed to be a Pawn. This includes non-combat support staff, combat troops, and secret agents. Some Pawns (especially more experienced ones) chafe at being referred to as such, but those higher up in the organization figure a little humility can't hurt (given the egos that sometimes show up), and that rising above being a mere Pawn gives agents something to aspire to.
Rumors have run wild over the years about the robotic duplicates that C.H.E.S.S. uses in various operations. C.H.E.S.S. allows the rumors to go (mostly) unchecked, figuring that misinformation about their capabilities can only work to their advantage. In truth, there have never been more than a dozen of these in operational use at any one time, primarily due to expense. The tendency for these units to seriously malfunction upon being damaged has been, for the most part, corrected. That said, their use is fairly limited - the main ongoing use is as a duplicate for the King or Queen (see below). These robotic servants also technically qualify as Pawns.
Bishops are operatives who possess some sort of paranormal mental ability, usually either telepathy, precognition, or postcognition. They usually do not function as field agents, and most have little to no offensive or defensive powers. Their primary role is to gather information, not to get involved in firefights. Much of the success C.H.E.S.S. has enjoyed can be traced back to information gathered by their telepaths, or being warned in advance of some terrible calamity by their precogs.
A small sub-branch of the Bishops include those who deal with magical phenomena. They are almost never actual spellcasters, but rather are those well-versed in occult lore, who can usually cast a number of various magical rituals if needed. The psychics and the magicians haven't always played well with each other in the past, but the two groups can usually put aside their differences when needed.
Knights are the elite combat arm of the organization, wearers of a formidable powered combat armor. There are only about a hundred or so of these suits in existence (they are hideously expensive to both create and to maintain), so there are usually only a few of these agents available in any given city. Those who become Knights were usually at least 5th level as Pawns, and also usually have to display a decent amount of technical expertise before being considered for this rank.
Rooks represent the best in the organization, with usually between two to three dozen agents at any given time qualifying as such. Pawns (and Knights who for whatever reason no longer wear the armor) must usually be of at least 8th level to qualify for this rank; Bishops who get more involved in field operations may qualify upon reaching 5th level. All Rooks have individual code-names, and usually have access to whatever cutting-edge technology that C.H.E.S.S. may have available at any given moment. Any superheroes that work with C.H.E.S.S. on a regular basis are often given honorary Rook status (but are not included in the number of agents listed above).
King/Queen represent the current leadership of C.H.E.S.S., the exact title depending upon gender. Congress must approve the appointment of any new King/Queen - in the past this has generally meant that those with more bureaucratic temperments were usually chosen, sometimes at the expense of those chosen actually having sufficient field experience. Internal C.H.E.S.S. regulations now require any potential King or Queen to have served for at least two years in one of the non-Pawn ranks (in practice, Bishops are virtually never considered for the leadership role, as there would appear to be a slight bias against those with any actual superhuman abilities taking control of the organization). Some have complained that this has swung the pendulum too far in the other direction, with the most recent Kings/Queens having too much of a 'cowboy' mentality.
CHESS Identicard design by Justice Carmon, based on Jeff Dee's fictional super agency presented in Villains & Vigilantes RPG