It'd be tricky, as the classes are designed to be interdependent. Many leader powers are of little use with no one to buff, and there's little point to a defender's mark when you're by yourself. Strikers and controllers are too vulnerable without a party.
I'd guess you'd need to do two things. 1) the player needs to pick a character who's abilities are all or mostly independent of other characters - that's most likely a striker, but I suppose a wizard qualifies, too. 2) the DM needs to scale encounters to fit the PCs abilities and general toughness. Thus, if the PC is a rogue, enoucnters can center around theft, sneaking about, disarming traps and taking individual enemies by surprise. For a ranger, it would be wilderness exploration, scouting, and tracking (and, again, what amount to assassinations). 'Chase scene' skill challenges, where the PC is the one being chased, would also be very apropriate. You could also take a standard adventure and just dial the threat-o-meter way down. That could work with a wizard. If an encounter retains the same number of enemies, but thier reduced in level and/or 'minionized' to 1/5th the exp guideline, a wizard might well be able to handle things. He hits easily, his lower-damage powers are still quite adequate because foes are so weak, he doesn't have to worry about catching allies in his AEs, and even though foes are weak, they're still a threat because he's 'squishy' for his level.
So, yeah, it could work: with a Striker vs mostly individual challenges of the right level, or a wizard vs more 'normally' structured challenges of substantially lower level. While a leader or defender might very well be able to handle such reduced-power challenges, as well, the fact that some of thier coolest features and powers just don't aply outside a group context would make them less satisfying to play solo.
Of course, if you really want the PC to play 'solo,' give him a Solo to play, and throw adventuring parties at him.