So I've been reading around, and I came across some methodology that suggested it is relatively straightforward to grow short carbon nanotubes. According to their recipe:
1) Construct vacuum chamber with heavy-duty anode and cathode within.
2) Bridge electrodes with carbon rod, evacuate atmosphere from chamber.
3) Arc 220V electricity through the carbon rod.
4) Carbon nanotubes will grow upon the anode.
5) Modulate chemical properties of carbon nanotubes by changing the atmosphere of the vacuum chamber. Apparently it's not so much important that there be no atmosphere as it is that there be no oxygen, which is fine by me as it is easier to build. Hydrogen makes sweeter nanotubes, while a nitrogen mix makes for more bitter ones.
It should probably be noted that I don't exactly yet know what it is I'm going to do with carbon nanotubes once I've grown them--in fact, that's an understatement, I have no clue--but that's not likely to stop me here. Now all I have to figure out is how to build a "vacuum" chamber. Maybe I can bribe a hacker with muffins to suck all the air out through a scuba mask regulator...