Chain Lightning has the following description:
You create a bolt of lightning that arcs toward a target of your choice that you can see within range. Three bolts then leap from that target to as many as three other targets, each of which must be within 30 feet of the first target.
The rules for damage rolls state:
If a spell or other effect deals damage to more than one target at the same time, roll the damage once for all of them. For example, when a wizard casts fireball or a cleric casts flame strike, the spell’s damage is rolled once for all creatures caught in the blast.
Assuming four available targets which of the following is correct?
- Roll once for damage for all of the targets
- Roll twice for damage, once for the first target, and once for the three subsidiary targets.
- Roll damage separately for each target
You only need to roll once for all targets.
The damage rule you've quoted handles this. Chain lightning is slightly more complicated than fireball or flame strike when it comes to determining who the targets are, but not so much so that the rules for how the damage gets dealt need to change. Even though you select them in two batches (the initial one target, and the subsequent 0-3), all of the targeted creatures are damaged at the same time, just like if they were in the area of a more traditional spell's effects.
For an example of when the rules do need to work differently, check out the chaos bolt spell from Xanathar's Guide to Everything. The spell does 2d8+1d6 damage if it hits its single target, and the important part of its rules for this question, are:
It specifically tells you that you should make another damage roll (and attack roll too) for the new target, since that new damage roll will determine if the spell leaps again or not. This is a more specific rule (specific to this one spell), so it overrides the much more general rule that you roll damage for all targets at once.