My own opinion, which I hinted at before (and Keith Pickering also pointed out), is the same general mechanism as for the model of the QBO -- but twice as fast. This idea essentially relates that the modulation of the yearly solar orbit (365.242 days) with the draconic (or nodal) lunar month of 27.21222 days sets up the perfect cyclic forcing for the 433 +/- 1.1 days Chandler wobble period.
Think in terms of the maximum declination of (1) the moon with respect to the equator along with (2) the maximum declination of the sun with respect to the equator. For (1) this happens once every ½ of the 27.2122 day nodal cycle or 13.60611 days and for (2) this happens twice a year (once for the southern hemisphere summer and once for the northern hemisphere summer).
Calculating this out, the closest aliased value is = 5.303 rads/year, equivalent to a period of 432.77 days. That is close to the generally accepted value of 433 days for the wobble . One can also produce this value graphically by sampling a sinusoid of period 13.60611 days every half a year (see below). That's enough to reveal the solar-lunar declination synchronization pretty clearly. In 120 years, I count a little over 101 complete cycles, which is close to the 433 day period.
The Earth has a large inertia compared to the moon, so it is essentially picking up differential changes in gravitational mass forcing, which is enough to get the wobble in motion.
So that's my simple explanation for what drives the Chandler wobble, yet this differs from Grumbine's idea, and from many other theories, many of which refer to it as a free nutation stemming from a resonance . I am closer to Grumbine, who thinks it is planetary-solar while I think it is luni-solar. Without getting into the plausibility of the gravitational dynamics, it's just too simple and parsimonious to pass up without posting a comment. It is also in line with my general thinking that very few natural processes follow a natural resonance, and that external forcing should always be the initial hypothesis. That works for the QBO in particular; in that case, the primary forcing period is the full Draconic cycle, likely due to the stronger asymmetry in lithosphere response for the two hemispheres.
And besides the QBO, this potential mechanism likely holds more clues to the behavior behind the ENSO model. As I commented at Grumbine's blog:
@whut said...The Chandler Wobble, QBO, LOD variation, ENSO, Angular Atmospheric Momentum, and oceanic and atmospheric tides all have varying degrees of connection, likely ultimately tied to luni-solar origins.
Keep plugging away at what you are doing because there are likely common origins to much of the behavior. If you can figure it all out, it will be useful in establishing the natural variability in climate, and thereafter the GCMs can then use this information in their models.
 435 days also happens to be a commonly cited number (see here), but I get the smaller 433 days when I look at the data myself . And Nastula and Gross recently came up with a value of 430.9 days from newly available satellite measurements.
 "On the maintenance of the Chandler wobble" Alejandro Jenkins http://arxiv.org/abs/1506.02810