You could use a the receptacle box as a junction box and run a cable over to the new light. You would also need to run cable for a switch unless the receptacle is already switched.

How did you turn on the "old" flourescent light fixture? Via a wall switch or a pull chain on the fixture?

I have florsecent fixtures in my garage that plug into a ceiling receptacle that is controlled by a switch.

There was a light switch that turned it on. However, the electrician had to pay a callback today and I checked it out with him. He did use the box as a junction box and I still have use of the outlet if I choose. Took him like 5 minutes. : ) Thanks!

Teresa