Run A 3 watt LED chip off a 12v Source
Typically, you want to use a switching or buck based led driver for this. Or you can use multiple 5W resistors in series/parallel. These will be cheaper. Especially if you want to use a 12V supply. A linear or resistive solution would be dissipating 9.8V at 0.7 Amps = 6.86 Watts.

A better solution is a 5V or USB supply. In this case, a cheap car usb charger would work best. It does the 12V to 5V with a switching regulator, and the rest can be done with a smaller resistor. 5 - 2.2 = 2.8V * 0.7 = 1.96W. A 2 or 2.5 Watt 4 Ohm resistor will work.

As mentioned 2.2V * 0.7A = 1.54W, half of the supposed 3 watts btw.