  Working in a three-dimensional variant of Winfree's abstract Tile Assembly
Model, we show that, for all $N \in \mathbb{N}$, there is a tile set that
uniquely self-assembles into an $N \times N$ square shape at temperature 1 with
optimal program-size complexity of $O(\log N / \log \log N)$ (the program-size
complexity, also known as tile complexity, of a shape is the minimum number of
unique tile types required to uniquely self-assemble it). Moreover, our
construction is "just barely" 3D in the sense that it works even when the
placement of tiles is restricted to the $z = 0$ and $z = 1$ planes. This result
affirmatively answers an open question from Cook, Fu, Schweller (SODA 2011). To
achieve this result, we develop a general 3D temperature 1 optimal encoding
construction, reminiscent of the 2D temperature 2 optimal encoding construction
of Soloveichik and Winfree (SICOMP 2007), and perhaps of independent interest.
