[Timeless Thinker]

Sodium chloride is added slowly to a solution that is 0.010 M in Cu+, Ag+, and Au+. The Ksp values for the chloride salts are 1.9× 10−7, 1.6× 10−10, and 2.0× 10−13, respectively. What will be the order of the precipitation of the metals, first to last? Explain or prove your reasoning.

It's just lowest Ksp precipitates firsts, right?
If so, then the order would be Au+, Ag+, Cu+

[Borek]

As a most obvious approximation, for identical initial concentrations of cations (as it is in this case) - yes.

To be sure it won't hurt to check stability constants for Cl^- complexes. I doubt they are high enough though.

[Timeless Thinker]

How would I check for that? Is there a formula?

[Borek]

If you have to ask it is probably beyond your current chemistry level.