Obstacles
Each obstacle requires a certain number of Chase Points to overcome. Typically, half the obstacles require 1 point fewer than the number of party members, and half require 2 points fewer (with a minimum of 1 Chase Point per obstacle). Particularly challenging obstacles might require more. Typically, there are multiple ways to overcome an obstacle; for example, characters could evade a security officer or give a bribe to ignore them. Each approach usually requires a skill check or Perception check, but sometimes a saving throw, an attack roll, or something even more unusual, like casting a certain spell.
On a character's turn, they describe what they do to help the group get past the obstacle. They then attempt any required roll, or perform the required action for a choice without a check. If they attempt a roll, the result determines how many Chase Points the character gains.
Chase Points represent the ability of the whole group to bypass the obstacle. A character who critically succeeds is able to help the other characters continue onward, while one who critically fails needs extra assistance. Players often have ideas for ways to overcome the obstacle beyond the choices you created for the obstacle. If their idea is applicable, you'll need to determine the DC and skill, or other statistic being used for that approach. This is great as long as it's creative, but be wary of a situation where a character who's legendary at a skill tries to justify how they can bypass every obstacle with that skill, such as using Acrobatics to tumble around them all, or the like. You can determine that some tactics just won't work against certain obstacles, or would help only one character without benefiting the rest and therefore aren't all that useful.
Once the PCs accumulate enough Chase Points to overcome the obstacle, they move on to the next. Extra Chase Points don't carry over to the next obstacle. However, anyone who hasn't already taken their turn that round can still take it against the new obstacle. Consequently, the characters best suited to overcoming the current obstacle might act first since the remaining characters might be better suited against the next one. The number of Chase Points the PCs have can never fall below 0.
It might help to put your obstacles in a stat block for easy reference. Inside published adventures, chase obstacles are likely to be presented in stat block form, as follows.
Crowd Obstacle 1
Chase Points 3; Overcome DC 15 Acrobatics or Athletics to weave or push through, DC 13 Society to follow the flow
Throngs of people crowd the space station corridors, making it difficult to continue the chase.