@oldturkey03 Agree 100%, the charger itself shows four different output voltages so it's pretty definite a control signal is needed.
As far as what goes where - that's a tougher question. I'm guessing blue is the V connection, and black is usually ground or the G pad. That would leave white as the D+, but of course then where is D-? You could check for continuity between D- and G on the Chromebook; if there's no resistance between the two then it's a good bet you don't need D- as long as G is present.
Another way to check would be to go back to the other end of the wires and see what they're connected to. That would mean opening up the power brick and tracing down the three wires to their source. I'm betting two of them will be together on a power board; those will be V & G. The other one should go to some kind of logic circuit that'll be controlling the output voltage.
With all that in mind, it's also possible that if there's a braided sheath over the three wires, it may also be part of the circuit. On Apple MagSafe chargers, that's actually the ground wire and you have to unbraid it then twist it together into a single wire for use as the ground connection. If that's what you find inside the power supply then the sheath should be G instead and the other non-power wire (black, probably) would go to D-.
As you can see, that's a non-standard setup; the wiring colors don't correspond to common USB cable usage, and the three wire configuration is just confusing things.
I'd love for anyone else knowledgeable about this sort of thing to jump in here and add your thought, since I'm mostly guessing at what's what.