I know, there is an analogy between RLC circuits and harmonic oscillators. Now there is a physical system, called double pendulum which has chaotic motion. I'm just curious if it is possible to create a circuit, which behaves like a chaotic pendulum, and use it for hardware randomization?
If you're looking to generate hardware random numbers and aren't concerned about double pendulums specifically, there are easier ways. See wikipedia for examples. One famous but impractical technique was Silicon Graphics' random numbers generated from a lava lamp.
Intel's Ivy Bridge processors use metastable R-S latches to generate true randomness from thermal noise. So if you just want hardware random numbers, your computer may have them already.
The double pendulum: -
I'm just curious if it is possible to create a circuit, which behaves like a chaotic pendulum
Yes you are watching it - your computer is a circuit and it is modelling it right in front of your eyes. Not only is this an answer, it is proof all in one package.
Of course, if you wanted to take the differential equations and do it using op-amps, this is also possible. Picture taken from this wiki page entitled double pendulum