Assuming you don't mind getting your thumb and forefinger dirty, you could do push the bottom of the chip bag up so that you can reach the chips without submerging your hand in the bag, which would get your knuckles all dirty. For detailed instructions, I like this video by Crazy Russian Hacker
However, if you don't want to get your hands dirty at all, there is only one way I've found. It doesn't work with all kinds of chips, just the ones that stick to your tongue or that you can grasp with your tongue:
- Pour some amount of chips into a bowl. This can be done without touching the chips at all.
- Hold the bowl with one hand
- Move the bowl upwards towards your mouth
- Stick your tongue out towards the chips, letting it touch one
- If the chip sticks to your tongue, great. Cheetos do that well. So does popcorn. If the chip doesn't stick to your tongue, attempt to grasp the chip with your tongue (probably requires a flexible tongue)
- Pull your tongue back into your mouth.
The chip should now be in your mouth and you can eat properly.
Note: when there are few chips left in your bowl, it starts to get awkward because you have to bury your face in the bowl and stick your tongue out really far. But hey, if we want clean hands...