Would it be in poor taste to ask my supervisor for a former coworker's schedule?

I currently work from 11:30am to 8:30pm. I hate this schedule. On of my coworkers, who works from 8:30am to 5:30pm, has recently been offered a new job and will be leaving within a few weeks.

I’d love to have an earlier schedule, but I don’t want to approach my supervisor about it if something like this would be crass. What’s your take?