The Chain Spell feat (Complete Arcane) causes a spell that normally has a single target to arc to multiple secondary targets based on your caster level. The spell chain lightning has a single initial target, then arcs to multiple secondary targets based on your caster level. If a wizard with a caster level of 20 memorizes a chained chain lightning how is the spell resolved (assuming thousands of available targets within range)? Does the feat go off first and then multiple secondary strokes move from there? Does the spell itself resolve first? Does it just double the number of secondary targets? Something else?
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I don’t think you can
Chain Spell says a spell that specifies a single target, and chain lightning specifies more than a single target. They don’t seem to work together.
The most reasonable interpretation, assuming you wanted it to work, is just to have two separate chains: the chain lightning one, and the Chain Spell one. Strictly speaking, though both specify that no target can be struck more than once, those are separate rules so someone hit by the original chain could also be hit by the Chain Spell chain, except for the first target. That doesn’t seem altogether unreasonable to me, balance-wise, but it does seem counter to the probable intent. Actually, combining them at all is probably counter to the intent and the actual wording.
I also think you can't but for a somewhat different reason than KRyan:
I would say the Chain Lightning spell is the result of someone incorporating the Chain Spell feat into the Lightning spell.
Since the feat doesn't stack you can't apply it again.
Edit: Yes, I realize the spell came first. I'm trying to make a reasonable interpretation of the situation.