TL:DR - We don't really know, but no, it's (probably) not chaotic.
First, let's notice that the definition of chaos given in the question is incomplete. As Ott puts it in a Scholarpedia entry, besides sensitivity to initial conditions, chaos is characterized by a "complex orbit structure" (see also the Wikipedia entry, answers in this site such as this, among many others).
Second, in principle this question cannot be answered, because all we know about the physics of "universe creation" is at best highly speculative.
That said, let's consider the question's assumption: there is a large, available parameter space of physical constants which contains a small region that results in a universe compatible with life as we know it. Then I'd say that, even if we accept this assumption, the answer is no, this isn't chaos here.
What's missing for chaos is the complex dynamics, some sort of aperiodic behavior: by assumption, once the parameters are fixed, the end state of the system is constant, either with or without life. So at most one could speak of final state sensitivity or, more appropriately here, structural instability.
Now, if we assume further that there is a dynamics of universe creation, where the physical constants are not parameters, but variables, then the interesting question (with respect to the anthropic principle) would be whether this small life-compatible region is an attractor or not - currently it's hard to even speculate about that. And, tangentially related to the original post would be the question of whether these varying physical constants do so chaotically - but so far we're not even convinced that they vary at all.