So, roughly roughly, you need to dissipate at least*** 6 watts of power....
***At least means that you may have to dissipate more to have a stable brightness. So, this is NOT "efficiently" as you suggested. There is only one way to do this efficiently, and this is with a buck converter. Of each of your LEDs requires 3.5V max, you will use a 3x3.5=10.5 (plus a few volts to increase switching speed) some 15-20 volts (or more of course). Then, you use a buck regulator with constant current output regulated at 1000 mA. You connect the LEDs in series and then connect this string to the output of the buck regulator. You can turn off an LED and keep all the other LEDs on simply by bridging its connectors. The regulator will then "see" this change and it will regulate the current again to 1000 mA.
I have used the A6210 for a similar project, able to drive up to 80Watts of LED with very high efficiency. It can operate up to 42V and deliver up to 3A of current. PLUS it has a PWM input which you can use to efficiently dim the LEDs. Here is a sample circuit:
http://www.pcbheaven.com/userpages/high_efficiency_high_current_led_buck_driver/(i think i've given it to you already

)
Where is the catch? The catch is that this driver comes only in QFN package. If you don't have a hot-air gun for re-flow works, you really don't wanna mess with this package. I used a QFN16 to DIP 16 breakout PCB to test in on the breadboard so don't be fooled by the images. The QFN is small, 4 by 4 mm in size and has 16 pads...
You can search for another similar chip in bigger package