Do the right-handed people tend to use the right side teeth of their jaw to chew food more often than the left-handed people?
Individuals have not only hand dominance but also a dominant foot, eye and ear. There has also been a belief that this sidedness applies to chewing as well. However, the short answer is that no one is sure, but that it may be related to handedness. I only looked at studies done after 2000.

One large study[1] found a questionable to weak correlation, not consistently maintained through different dentition (baby teeth, mixed, and permanent). A slightly smaller study showed a correlation; in 78% chewing side preference correlated with other tested lateralities (footedness, handedness, eyedness and earedness).[2] Another similar sized study found none.[3]

A small 2012 study found that there was a preference for right sidedness when chewing hard food (73.68%) and for soft food (57.89%) but failed to correlate this with hand/other-sidedness.[4] Another small study tested for sidedness, finding that 55% of subjects did not have any side preference, 30% preferred to chew on right and 15% preferred the left side, and this was reproducible in 90% of subjects only with almonds (a medium hardness food) as opposed to jerky or asparagus. Unfortunately they did not measure sidedness. Their findings were that chewing-side preference is not a fixed characteristic, and texture seemed to affect sidedness.[5] A review article determined that a person's dental condition to a large extent dictates how they chew.[6]

The studies were mostly designed very differently, making good comparisons difficult. I think it's safe to say it's possible but not known with certainty.

[1] Absence or weak correlation between chewing side preference and lateralities in primary, mixed and permanent dentition
[2] Chewing side preference as a type of hemispheric laterality
[3] Relationship between chewing side preference and handedness and lateral asymmetry of peripheral factors
[4] Chewing side preference in first and all mastication cycles for hard and soft morsels
[5] Chewing-side determination of three food textures
[6] Adaptation of mastication in response to the characteristics of the individual or the food