I think it is certainly appropriate to denote as a "grand project" the remarkable new progress in the area sometimes called additive combinatorics or additive number theory, though the subject has expanded to the point that neither of these are good names any longer, if they ever were. I am talking about the strain of thought whose modern form starts with Gowers and continues through with work of Tao, Green, Helfgott, Breuillard, Ziegler, Pyber-Szabo, and many, many others: loosely speaking, all this work centers around the idea that "things that are approximately structured approximate a structure" -- so that if I am a subset of a group and I am approximately closed under multiplication, I must be close to some literal subgroup; or if I am a subset of Z which contains too many arithmetic progressions, I must actually have big intersection with some infinite arithmetic progression; or if I am a subset of R^2 such that lines containing two points of my set are overly likely to contain a third, then I must look something like a subgroup of a real elliptic curve....
Another way to put it is that this field is concerned with structural dichotomies -- subsets either obey the laws that completely random subsets do, OR they are "structured" in some appropriate way; there is no in between.
To me this perfectly meets the definition of a grand program -- like Gromov's take on group theory (with which it shares both some content and some philosophial affinity!) it provides a really new paradigm for "how things are," and at the same time it has given us real progress in a multitude of areas (analytic number theory, harmonic analysis, combinatorial geometry, etc.)