Level 100 Statistics (see level 5, 50, 100)
Hitmonlee is actually pretty good. In UU, it is a force to be reckoned with.
Use this Choice Band set how you would any other Choice Bander, with one important proviso: Hitmonlee can also switch into paralyzing moves such as Thunder Wave with impunity, since it has the Limber ability. Rock Slide isn't particularly useful in UU, as even Focus Punch hits Gligar harder on the switch, but it is useful for Pinsir and Scyther.
Substitute or Endure to get your Salac Boost and then attempt to sweep. This is a pretty simple and standard strategy, but again Hitmonlee's Limber ability is extremely useful for this set.
Bulk Up can be used with either Substitute or Endure, but Focus Punch should be used with Substitute. If you are using Bulk Up, you may want to lower your Speed to 254 Speed (176 EVs) and put the rest into HP so you can potentially get 2 or more Bulk Ups, as this still allows you to outspeed everything in UU but Timid Electrode, which is extremely rare.
It can Double Kick for stuff like Substitute Aggron, but it's not that useful. It can use Return to hit Gligar harder than any of your other moves.
Attack and Speed, only.
Checks and Counters
Gligar is the best counter, thanks to its high Defense, Flying STAB, and Hitmonlee's low Defense. Slowking will also have a thing or two to say to it. Masquerain beats those without Rock Slide. Blastoise and Meganium can take hits from the Choice Band set. Grumpig and Hypno can use it to set up Calm Mind with their Fighting resistance, but Hidden Power Ghost will put the hurt on them.