Install page template along with my plugin?

I’m developing a plugin that requires a page template to be present in the theme. How can I ensure that the template gets installed at the same time as my plugin? I don’t want to burden the user with an extra installation step.

I was thinking I would create the template file and write to it from within my activation method, but I don’t see a way to do that. Makes me think that maybe that’s not the right approach.

Any suggestions on how to accomplish this?
Thanks
Ken