If you have a broken LED Christmas light, the first step is to identify the problem. Check the string of lights for any visible signs of damage, such as a loose connection or a burned-out bulb. If the string is still functional but one light is not working, you can use a multimeter to test the resistance across the non-working light. If the resistance is infinite, the light is broken and needs to be replaced. You can also try using a continuity tester to find the exact location of the break in the light's circuit.