Early embryonic patterning events are strikingly precise, a fact that appears incompatible with the stochastic gene expression observed across phyla. Using single-molecule mRNA quantification in Drosophila embryos, we determine the magnitude of fluctuations in the expression of four critical patterning genes. The accumulation of mRNAs is identical across genes and fluctuates by only ∼8% between neighboring nuclei, generating precise protein distributions. In contrast, transcribing loci exhibit an intrinsic noise of ∼45% independent of specific promoter-enhancer architecture or fluctuating inputs. Precise transcript distribution in the syncytium is recovered via straightforward spatiotemporal averaging, i.e., accumulation and diffusion of transcripts during nuclear cycles, without regulatory feedback. Common expression characteristics shared between genes suggest that fluctuations in mRNA production are context independent and are a fundamental property of transcription. The findings shed light on how the apparent paradox between stochastic transcription and developmental precision is resolved.