The LED will begin to glow a bit before the current limit is reached.
Can you please tell me why the led has to be placed in parallel with the resistor and not is series?
Here's my take on that circuit...
R3--the 220 ohm resistor--is there to give a path for the current when the transistor is on but the voltage across the LED isn't enough to illuminate it. The transistor comes on when there is ~700 mV dropped across the current sense resistor (R1.) The LM317 isn't in current limit mode until the drop across R1 is 1.25V, however, so the LED shouldn't be illuminated just because the transistor is on. So the 220 ohm resistor will give a path for the current.
So when does the LED come on? And how does its illumination happen to coincide with the LM317 being in current limit mode?
First, remember that red LEDs require approximately 1.8V across them before they will illuminate. The voltage drop across the LED is playing an important part in this circuit. A different colored LED might not work due to it having a different V
f.
Now, if you look at the datasheet for the LM317 you will note that the minimum dropout voltage of the part is between 1.5V and 2.3V--depending on the current and the temperature. This is basically due to the fact that the series pass element is a Darlington pair.
So, if you add the 1.25V drop across the current sense resistor and the 1.8V drop across the red LED that just so happens to be in the same neighborhood as the voltage that indicates that the part is in current limit mode.