At a minimum this needs to have:
obstacles, generating them during play if the chase isn't going through a detail-mapped area - giving an advantage to nimble or athletic racers
fatigue, giving an advantage to fit racers
things that end the chase - the chase leader disappearing from view and being untrackable by sight, or deciding to hide; at which point the chasers have to either split up or use other tracking and detection means. Also rules for what happens when the chasers catch up.
So here we go...
Layout of the chase: At the point where one group or individual flees an encounter, and an enemy group or individual pursues, create a chase track of about 20-50 spaces where each space = 10' (using a battlemat, Snakes and Ladders board, etc.; or just use percentile dice to represent their distance along the track). Lay out the fleeing and pursuing figures representing the relative distance between them. To save space on the track, you can assume that a figure must move 12 spaces just to stand still, and move them backwards or forward on the track according to how much they exceed or fall short of this number.
Conducting the chase: First the fleeing, then the pursuing figures move. Each fleeing figure rolls 1 d6 for each 3 points (30 feet) of movement he or she has.
For each die that rolls 1, the figure moves ahead 2 spaces.
For each die that rolls 2-5, the figure moves ahead that number of spaces.
For each die that rolls 6, the figure makes a Body save (aka Fortitude, Poison). If it succeeds, it moves 6, if it fails, it gets fatigued, moves only 3, and has a -1 to its movement rate in future rounds (that is, subtract 1 from the number of squares moved on any die roll). Penalties from multiple failed fatigue rolls add up. Staying in place for 1 round removes all fatigue penalties.
Movement Obstacles: These procedures generate random terrain for areas of the chase you don't have closely mapped. You can use the rules for how these obstacles affect pursuit even if you have them mapped out already.
Rolls of 1 made by the leading figure may create Movement Obstacles. If running across flat ground (dungeon floor, plains) the leader creates one obstacle for every 3 1's rolled. If running across ground with some obstacles (shrubs, fields, bumpy floor) he or she creates one obstacle for every 2 1's rolled. If running across ground with many obstacles (forest, city alleys, busy streets, jagged ground, swamp), one obstacle is created for every 1 rolled. Put the obstacles separately in the spaces right in front of the leader before he or she moves.
Each obstacle requires the leader to make a Speed save or have -3 movement that round, to a minimum of 0. Pursuing figures must make the same save when moving through an obstacle. If you're subtracting 12 movement spaces from each figure, this would make the obstacles travel backwards on the track 12 spaces per round.
Losing Sight: At the end of a round after everyone has moved, roll dice to see if the pursuers have lost sight of the pursued, who may have disappeared around a corner, over a ridge, or behind some foliage. The DM rolls a number of d6 that will tell how many 10' spaces the leading pursuer can see ahead in the environment. If this is less than the distance to the last fleeing figure, sight is lost.
Flat, clear land: d6+100 spaces
Low hills: 3d6 x 2 spaces
Steep hills/mountains: 3d6 spaces
Light forest, city streets, light mist: 2d6 spaces
Heavy or hilly forest, city alleys, heavy fog: d6 spaces
If the total dice roll is even and sight is lost, the pursued figure may try to hide on the spot, subject to skill resolution. If the total dice roll is odd and sight is lost, there is an opportunity for the leading figure to go one of two ways and not be seen in the act; pursuers must then try to track their quarry, or split up to continue the pursuit.
Next up: Some issues in representing this all visually.
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