Sean,

For that circuit in AoE, you need to be driving it or it will oscillate.
In other words, if you have no input signal then the feedback resistor
provides the input. Now, since hc04 is an inverter, the output is opposite
the input. If the input is low the output is high ... Now the feedback
resistor will try to change input to the opposite state. So if the outpu
goes high then the input is pulled high, which will cause the output to
go low, which will pull the input low, .etc


In your case, you'll want to provide an AC signal all of the time.  In
fact, AoE states that this circuit is intended to generate a 10Mhz sq wave
from a 10Mhz sine wave.

Scott