Chargebacks aren't available at the task level, this functionality is only available at the project level. However, an option to workaround this behavior would be to use charge codes in conjunction with Chargebacks to get the total cost for a Department.
Here's an excerpt from an answer supplied in a CA Communities post including the additional option of a custom attribute: Can you chargeback specific tasks?
"You might want to use the OOB functionality where an entire project is allocated on a percentage basis for most projects. But, for your maintenance projects, set up charge codes that correspond to your Departments. Then, with reporting you can combine the costs allocated via the OOB charge-back functionality with the costs associated from the Charge Codes to get a total cost to a Department. And, one of the advantages of using Charge Codes for such cost capture is that you get explicit costs as opposed to a percentage allocation.
Another advantage of using Charge Codes for more sophisticated cost capture is that it allows asymmetric cost capture. For instance, if within a development project certain specific activities are being funded by a given department, you can use charge codes to show those cost charges to that department.
Another alternative might be to create a custom attribute on the Task that uses the Department look-up (especially useful when there might be multiple departments responsible for the activity). Again, reporting can be used to combine these costs with standard project costs. The disadvantage to this approach is that the custom attribute will not be in the WIP table, with the controls associated with the WIP table."