Hmmm... well if you can find a chip to do it, you could consider using stepped resistors, so if you calculated out how powerful a resistor would have to be in order to fade the LED, you could use a counter that would bounce up and down, so say you've got 10 resistors from 1Kohms to 10K ohms, you could set up the counter so it would go...
1234567890987654321234567890987654321 and so on, and each value would then tell the chip which output to use, something like a binary counter could be modified to work.
Sure with resistors only up to 10K, it wouldn't fade too much, but you could alter it, like a 1K, 10K, 25K, 50K, 100K, 250K, 500K, 1M, 1.5M, 2M (almost unlit)