Depending on your skill set and junkbox, there are so many ways of working this out. If you are so inclined, throw a Raspberry Pi at the challenge. The Pi can handle very complex control strategies and be the source of the chime. Hardware costs would be minimal.

In the most basic schemes the power up delay of the amplifier will be an issue. You can work around this with a very small modular amplifier that the experimenters would use in their projects. Switch the speakers to this amplifier while the chime rings -- just pick an amplifier that starts up promptly. Even with all this fuss your hardware costs could be under $100.