I don't believe anything is built in that will do this however I use a great free tool called Paymo (http://www.paymoapp.com/) that I launch at the start of working and it runs in the bg using little to no cpu or ram and it not only tracks the time but allows projects to be managed and the time can be reconciled against budgets as well as auto generate invoices. You of course have to remember to start and stop the app, where a built in tool tied to launching the program or a project, like that of Quickbooks would obviously be more automated and perhaps what you are ultimately seeking, however in lieu of that check out Paymo its reporting gives a very slick and professional way to present to your client.
That's awesome !
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Time tracking (to produce billable hours) within Adobe programs is is a GREAT IDEA and very doable. Third-party plug-ins do this but are expensive -- it's time Adobe made it an option within the Creative Cloud. To manage the "idle time" issue, the clock would stop ticking after a designated amount of time where no activity is happening within the program. It would resume as soon as new activity begins. The "duration time until idle" would be set within preferences. The tracking program would create a report showing each Adobe software with active time listed by project. You could drill down for time details. Simple. DO IT ADOBE!