While I was looking through the Pathfinder GameMastery Guide I found the Chase encounter rules. It had separate options, DCs for certain obstacles, different starting positions depending on the situation (all great things), but no notes on overall or per-obstacle Challenge Rating. So, How does CR apply to obstacles in a chase? If it doesn't, How much experience does a PC get for a mandatory skill check?
I suggest using the difficulty to resist monster abilities by CR to approximate a value.
First, calculate the average DC of all the checks in the chase.
Then compare that DC with the Primary Ability DC in the Table: Monsters Statistics by CR of the Bestiary. That will give you a CR you can convert to experience points.
Because the more checks you have to perform, the more difficult to succeed in the chase, I would consider this CR value adequate for a 10 cards chase. If you use less cards, decrease or increase by 1 the CR for each 5 cards less or over those 10 standard cards.
Keep into mind this is just a guide, and as a GM you should adjudicate whether the calculated result is appropriate and take into account situations that might lessen or increase the difficulty of the encounter.
I have run a few chases in the past, and I usually assigned XP to the party as if the chase itself were its own combat encounter. I looked at the difficulty of the DCs that I assigned for the various skills and compared them to the level of the PCs and also based it upon how difficult it was for them to actually accomplish and manage the chase. Having done that I then awarded XP for a combat equal to CR or +1/-1 depending on how things went.
I couldn't find anything in the Game Mastery Guide or online either.