What do I need to drive my big LED chip?
To keep it simple lets just say you have three 3 Watt LEDs, an R, G, and B.
I assume you want to adjust the current in each LED to get the same functionality as a Phillips Hue light bulb.
It is easiest if you find green and blue LEDs with a forward voltage below 3V which is just under the 3.2V cutoff discharge voltage of an Li-ion battery.
Rather than an RGB I would recommend using the Luxeon C Color line LEDs.  They are small, have excellent color mixing, and very wide viewing angle (170°).  Some good alternatives are the OSRAM Oslon SSL 150 and Cree XP-E and XP-E2



If you are stuck on a single RGB then I would recommend the LED Engin LZ4 which is an RGB and White.  You do not have to use the white.



You will need three LED drivers, one for each color. Here you have to design your own or use an off the shelf DC-DC constant current buck step down driver.  If your forward voltages get too high then you'll need a buck-boost constant current driver.
The only off the shelf driver I would use would be the Mean Well LDD (buck) or LDB (boost-buck) but they have a minimum input voltage of 9V.  You could use 3 batteries in series.  The efficiency of the LDD driver is 97% so you will still be using most of the battery's energy to drive the LEDs.

The big problem with LED drives is the overhead voltage required. Some buck drivers need 4V over the forward voltage.  You need a driver with a very low overhead or use serial batteries.
There are two methods you can use to dim the LEDs.  PWM or a varying voltage level.
If I knew more about your application and you had the desire to design your own driver I could recommend some driver chips.

If you were to go with a NiMH or NiZn rather than Li-ion you could use a very simple boost driver.  The Nickel-zinc (NiZn) is an excellent LED battery with a very flat discharge curve but best of all it is 1.65V rather than 1.5V.
Microchip Boost Driver