Random timed output circuit
If you generate a high(ish) frequency square wave (1kHz or above) with a 555 and feed it into a counter circuit, you can use another 555 set to a frequency like 0.5Hz to latch the outputs of timer every 2 seconds.

You'll need two 555s, a free-running counter and a latch circuit.

The chances are the three outputs you will get will be pretty random.

Here's the counter: -



And feed three of its outputs into the latch: -



The three outputs (aligning with the three inputs from the counter) can be used to drive a few mA into 3 LEDs.