Process won't let go of deleted file.

There's a mission critical service that really can't be stopped. The log was getting big, so we decided to manually rotate. The log file was deleted before the service was HUPed. Now, the process is still writing to this deleted file in /proc/123/fd/1. I tried HUPing, but it won't stop writing to it. I'd like to make the process open a new, real file on disk without stopping it. Is this possible? Running CentoOS 6.5. Thanks.