And vice versa, do the left-handed people tend to use the left side teeth of their jaw to chew food more often than the right-handed people?
Or the frequency of food chewing distribute fairly to both sides of the jaw?
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 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). Another similar sized study found none.
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. 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. A review article determined that a person's dental condition to a large extent dictates how they chew.
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.
 Absence or weak correlation between chewing side preference and lateralities in primary, mixed and permanent dentition
 Chewing side preference as a type of hemispheric laterality
 Relationship between chewing side preference and handedness and lateral asymmetry of peripheral factors
 Chewing side preference in first and all mastication cycles for hard and soft morsels
 Chewing-side determination of three food textures
 Adaptation of mastication in response to the characteristics of the individual or the food