Possible to built 555 timer/led circuit that is 1 hour on, 11 hours off?

Need advice. I'm trying to make a wall clock and am planning to use LED's to light up certain areas of the clock during different hours. For example, at 2pm the area under the "2" on the clock would light up and stay lit and/or flash for 1 hour, then at 3pm the "2" light would turn off and the "3" light area would turn on. That would continue to cycle through 12 hours then restart. Is that possible?

I'm an engineer but not electrial. I have taken an EE class in college several years ago. Comfortable with circuits, wiring a breadboard, sizing resitors and capacitors, etc. I just don't know if I'm going about this all the wrong way. I can't find any solid information on the googles on the limits (as far as time/duration) of 555 timers. I've exhausted sparkfun.com, buildcircuit.com, instructables.com, mdfly, and a slew of other websites.

Is this possible or should I start focusing on an arduino board and programming that? Any suggestions or ideas are welcome.