You can create a default "No Charge" item, which can be applied to time entries. It will automatically set the hourly rate to $0, while the time entry will still appear on the invoice.
To apply a "No Charge" time entry, follow these simple steps:
1) Click on "More", and select "Items", or click here.
2) Select "New Item".
3) Title this item as "No Charge" with a "Price" of $0.
4) Switch "Use Item Price Instead Of Hourly Rate?" to "Yes", and click "Save".
What Happens Now?
Whenever you need to create a time entry with no charge, make sure to select the "No Charge" item. These time entries will still be billable, but they won't add to the total balance due.