Does the caster choose all targets or only the initial one?
Must the secondary targets be in the caster's line-of-sight?
I'm probably way over thinking this, but the 6th-level chain lightning spell description states, in relevant part:
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. A target can be a creature or an object and can be targeted by only one of the bolts. [Emphasis added] (PBR, p. 85; PHB, p. 221)
Only the initial target is specified as being seen and the choice of the caster. However, since "a creature or an object" can be a target, there could be nearly limitless secondary targets within 30' of the initial one (e.g., bricks, rocks, leaves, etc.). The language "can be targeted" may imply that the caster is the one doing the targeting, but the fact that the caster may not have three secondary targets and exactly three bolts (not up to three bolts) come from the initial target seems to suggest that the bolts do the targeting (either randomly or by conductivity, etc.). This language is somewhat contradicted and confused by "as many as three targets," yet definitely three bolts.
If the caster chooses the secondary targets, and line-of-sight is not required, does this mean a caster could hit creatures around corners or behind barriers by simply by targeting an initial object within 30' of the actual unseen targets? For example, targeting the sconce at the bend in a dungeon to hit three creatures around the corner, or targeting a closed door (or doorknob) to hit three creatures in the room on the other side?