Boundaries in three-dimensional mathcal{N} = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits mathcal{N} = (0, 2) or mathcal{N} = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For mathcal{N} = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.