I have an HP Chromebook and a Nexus 6P smartphone, and both of them use USB-C connections for charging. When I plug the Chromebook into the Nexus's charging cable, it works fine and I just get a message that says I am connected to a "low-power charger". However, is it safe to plug the cell phone into the laptop's power supply? I'm afraid that doing so might fry the phone.
Type-C original specifications (and Power Delivery specifications over Type-C connector, if any) are designed precisely for the sake of compatibility and inter-operability. Since both Type-C devices come from reputable manufacturers, I would expect that they are compliant to all related specifications, and no harm will be done to any of your devices.
The message from Chromebook means that the Nexus charger has either basic charging capabilities, or less capabilities than is expected by Chromebook.
This means that the Chromebook charger has more capabilities than the basic "safe" power delivery. However, the Nexus phone, assuming it is designed correctly, should negotiate only what it needs, and the Chromebook charger should provide what Nexus is asking for, and nothing more. So it should be perfectly safe to use Chromebook charger for Nexus phone.
This is the entire idea behind intelligence that is built into Type-C power delivery.