How accurate does this timing need to be? I think 24 hours is very close to, or beyond the limit of that a 555 timer will allow (due to capacitor leakage and tolerances and things like that).
You could make a simple PIC circuit with a very slow oscillator and store the counts in a massive register to count to 24 hours. THat would be very, very accurate. At 26MHz frequency, a 39-bit counter is enough to track 24 hours. You'd basically have to link together a giant series of integer variables together in memory since 8-bit MCUs don't have large enough counter registers that periodically get updated by a timer (a dsPIC timer counter can do this though if you use the 32-bit timer and a 256:1 prescaler, it can actually go up to 48 hours like this on a clock of 6.5MHZ x4 PLL).
Do you need the signal to go HI for 24 hours and then go LO for 24 hours? Or to pulse HI momentarily and then go LO, and then do so again 24 hours later?
You could also hack an alarm clock or stopwatch or something.