It may sound straight forward, but I've read the spell's description about twenty times now and it doesn't specifically say.

Chaos Bolt (XGtE, p. 151)

You hurl an undulating, warbling mass of chaotic energy at one creature in range. Make a ranged spell attack against the target. On a hit, the target takes 2d8 + 1d6 damage.

If you roll the same number on both d8s, the chaotic energy leaps from the target to a different creature of your choice within 30 feet of it. Make a new attack roll against the new target, and make a new damage roll, which could cause the chaotic energy to leap again. A creature can be targeted only once by each casting of this spell.

You roll the attack, and let's say it hits. Then you roll 2d8+1d6, let's say both d8s are 5, meaning it would jump.

Here's the question. Does the damage resolve on the first target THEN attack the second and resolve on the second as well? Due to the "wild magic" perception of this spell, it would "hit" the first guy, but not damage him, instead moving to the second guy, until finally you stop rolling doubles.

Example:

I'm attacking Bob (because screw Bob), and he's got his buddies Ted and Dan. I roll to attack Bob, hit, roll damage: result is 8+8+6 (max damage, because Bob deserves that). That would mean it would jump to let's say Ted (because screw Ted). Would Bob take the 8+8+6, and then I would roll to hit and damage Ted,

OR

would the damage to Bob not happen, and INSTEAD I would roll to hit and damage Ted?

On a hit, you deal damage

The spell states that, "on a hit, the target takes 2d8 + 1d6 damage". Nothing later in the spell contradicts this, so no matter what you roll on the dice, the target takes damage. Then you might make another attack roll etc., but that doesn't change the initial attack.

If the Bolt only bounces and doesn't deal damage, it is strictly inferior to Chromatic Orb

Chromatic Orb is another 1st level spell that Sorcerers get access to. It does 3d8 damage of the type you choose. If Chaos Bolt didn't do damage on a bounce, it would do less damage, have an uncontrollable type, and target unpredictably, making it worse in every way to Chromatic Orb. The fact that it can chain and do more damage to more targets is what makes it viable (and fun!).

The 5e developers generally don't make options that completely invalidate other options, and they wouldn't introduce one like Chaos Bolt in a supplemental book when Chromatic Orb was already in the PHB. They certainly make mistakes from time to time but this seems like an obvious one, and the fact that an un-chaining Chaos Bolt would be useless adds weight to the reasoning I used above.