Can't get this schmitt oscillator to work...did I goof somewhere?
You schematic is 100 % accurate. 

Funny thing is that on a simulator, if all the thresholds and RC values are identical, it won't startup as all LED drivers go high and low at the same time.  This circuit works by the voltage difference between stages and can drive about 7mA.

So just change any part a bit in value and be sure to have a cap across IC for noise reduction and keep wires as short as possible. 



Choose any reasonable RC=T product. I used T=RC=0.1s which with Schmitt thresholds can yield 1.6Hz for 3 stages.