First I will answer the question in the title. You are asking about nuclear chain reactions.
Now if nuclear chain reactions were not possible, then the proton proton chain reaction would not be possible either, that is one of the two known sets of chain reactions by which stars transform hydrogen into helium, like our Sun.
The proton–proton chain reaction is one of two known sets of nuclear fusion reactions by which stars convert hydrogen to helium. It dominates in stars with masses less than or equal to that of the Sun, whereas the CNO cycle, the other known reaction, is suggested by theoretical models to dominate in stars with masses greater than about 1.3 times that of the Sun.
Although often called the "proton–proton chain reaction", it is not a chain reaction in the normal sense of the word (at least not branch I – in branches II and III, helium, which is the product, also serves as a catalyst). It does not produce particles that go on to induce the reaction to continue (such as neutrons given off during fission). In fact, the rate is self-limiting because the heat produced tends toward reducing the density. It is however a chain (like a decay chain) and a reaction, or more accurately a branched chain of reactions starting with two protons coming together and yielding deuterium.
Now you are asking about nuclear fission.
When an atom undergoes nuclear fission, a few neutrons (the exact number depends on uncontrollable and unmeasurable factors; the expected number depends on several factors, usually between 2.5 and 3.0) are ejected from the reaction. These free neutrons will then interact with the surrounding medium, and if more fissile fuel is present, some may be absorbed and cause more fissions. Thus, the cycle repeats to give a reaction that is self-sustaining.
You are saying that the laws of physics would change so, that the fission itself would not happen. This could mean too that decay would not be possible, and molecules chemical reactions would not be the same (and so the matter around us would not be the same). We would not have electricity (currently based on these power plants), and because we would need power plants based on cole (and other pollutive sources) the environmental pollution would be much higher.