Yes, a kitchen chimney can run on inverter. However, it is important to keep a few pointers in mind before connecting the chimney to the inverter. The total power consumed by the chimney must not exceed the total load handling capacity of the inverter. If it does, then your inverter will not be able to handle the load and will trip. Also, it is important to ensure that the power of the inverter is between 600 to 800 VA.