Based on official Pathfinder Chase rules, but with some logical fallacies adjusted and the overall rules simplified.

Building the Chase

• Choose a base speed for the chase; this should probably be whatever is the most common speed for all the participants. Each obstacle will be approximately this far apart
• Lay out a series of obstacles with a Standard (~50% chance of success) solution and an Accelerated solution (harder)
  • For level 1 characters vs a goblin, I did DC10 for Standard, DC15 for Accelerated for most solutions
  • The Standard solution is the "most obvious" way of overcoming the obstacle; the Accelerated solution is a clever or more difficult way of overcoming the obstacle quickly.
  • Example: climbing a wall (Standard) vs doing a parkour jump over it (Accelerated)
• Sometimes you may want to introduce an "Automatic" solution, which symbolizes something that you can't fail at, but may take longer (e.g. instead of going over the wall, go through the gate). To account for the lost time, the PCs takes a fixed penalty on the next check
• Ideas for obstacles and solutions: https://olddungeonmaster.com/2015/01/17/dd-5e-quick-reference-chase-rules/

Running the Chase

How I explained the rules to my players

For a chase, you will go through a series of discrete challenges with bonuses based on your skill modifiers and your speed. Anybody faster/slower than 30ft per round? Take note of +/-2 modifier per 10ft. You will be given two options to overcome each obstacle: one standard, one accelerated. If you succeed at the standard option, you progress to the next obstacle. If you take the accelerated option and succeed, you can try the next obstacle with disadvantage. This bonus does not chain. You are welcome to come up with your own alternative solutions to the obstacle, and I will decide if it is standard or accelerated. If you fail any obstacle, you are stay there and can retry on your next turn. You are also welcome to take any other standard action, as the obstacles are just move actions (though double move isn't allowed).

The rules in bullet form

• Base Speed: 30ft; +/-2 to skill check for every 10ft faster/slower
• You can either make the normal action or you can make the accelerated action; if you succeed at an accelerated action, you can try another action with disadvantage (roll twice, take the worse roll; doesn't chain)
• Impromptu DCs: DC10: Trivial; DC15: Simple; DC20: Standard; DC25: Hard; DC30: Very Hard
• For "super trivial" solutions, you could instead have an Automatic Success with a penalty on the next obstacle (e.g. making up lost time) and a Standard solution to avoid the penalty.
• TODO Should obstacles count as standard actions or just move actions? "Depends on the obstacle" seems too complicated, but "find the lost trail" seems like it deserves a standard action
• Ad-hoc adjust DCs for clever solutions that aid the other players (e.g. "hey, come this way!" or "I leave the rope and grappeling hook behind")
• If a player gets stuck on a single obstacle for too many rounds, you can lower the DC to account for progress made on previous attempts,

Example Chase

Goblin, Bestiary 156
Reflex Save: +2
Relevant skills: Acrobatics +2, Climb +0, Escape Artist +2, Knowledge(Nature) +0, Perception -1, Survival -1, Swim +4
Concealment: 20% miss chance for all ranged attacks from within 60ft; 50% miss chance for all ranged attacks from >60ft
Melee attacks allowed if you are in the same square

1. Cross the river
   • Run across the tree: Acrobatics DC10
   • Ford the river: Swim DC15 (and take another action with disadvantage)
2. Lost trail in the forest
   • Follow the trail: Survival DC10 (Very soft ground, moving at normal speed)
   • Catch a glimpse through the trees: Perception DC15 (and take another action with disadvantage)
3. Up the embankment
   • Climb the embankment: Climb DC15 (wall with handholds)
   • Parkour up the roots: Acrobatics DC20 (and take another action with disadvantage)
4. Through the brambles
   • Search for path through: Survival / Knowledge Nature DC15 (in hindsight, this was probably too difficult)
   • Dive/Slide through hole: Escape Artist / Acrobatics DC20 (and take another action with disadvantage)
5. Down the muddy slope
   • Slide down the face: Automatic Success, but +3 DC on next obstacle due to mud in your eyes; and you are considered flat-footed for combat
   • Fall with Style: Acrobatics / Reflex Save DC25 (describe your success and take another action with disadvantage)
6. Boulders in the way
   • Go around: Automatic Success, but +3 DC on next obstacle trying to make up lost time
   • Climb over: Climb DC15 (wall with handholds)
   • Squeeze through gap: Escape Artist DC20 (and take another action with disadvantage)
7. The goblin gang's campsite (read campsite description now)
   • Run right into the group: surprise round; you are by yourself
   • Make a tactical entry: Stealth DC20; no surprise round (gang is aware you are coming unless you killed the goblin)

Alternative Rules

Official Pathfinder chase rules: This is what I used as my foundation and then just dropped the things that didn't make as much sense to me or were forgotten in the design process. I wasn't a fan of the "clear two obstacles and skip the next" because it is hard to justify why that works, so instead I introduced Accelerated actions and pulled the 5e concept of disadvantage to provide a reasonable penalty on the next check.

Geek Related's chase rules: These rules have a large number of modifiers and math, which seemed far too complicated for Session 2 with a group of new players (and a new GM!). Maybe I'll give these a shot when we are more comfortable with doing skill checks and lots of math.