As the Drosophila embryo transitions from the use of maternal RNAs to zygotic transcription, domains of open chromatin, with relatively low nucleosome density and specific histone marks, are established at promoters and enhancers involved in patterned embryonic transcription. However it remains unclear how regions of activity are established during early embryogenesis, and if they are the product of spatially restricted or ubiquitous processes. To shed light on this question, we probed chromatin accessibility across the anterior-posterior axis (A-P) of early Drosophila melanogaster embryos by applying a transposon based assay for chromatin accessibility (ATAC-seq) to anterior and posterior halves of hand-dissected, cellular blastoderm embryos. We find that genome-wide chromatin accessibility is highly similar between the two halves, with regions that manifest significant accessibility in one half of the embryo almost always accessible in the other half, even for promoters that are active in exclusively one half of the embryo. These data support previous studies that show that chromatin accessibility is not a direct result of activity, and point to a role for ubiquitous factors or processes in establishing chromatin accessibility at promoters in the early embryo. However, in concordance with similar works, we find that at enhancers active exclusively in one half of the embryo, we observe a significant skew towards greater accessibility in the region of their activity, highlighting the role of patterning factors such as Bicoid in this process.