Sex chromosome dosage compensation is essential in most metazoans, but the developmental timing and underlying mechanisms vary significantly, even among placental mammals. Here we identify human-specific mechanisms regulating X chromosome activity in early embryonic development. Single-cell RNA sequencing and imaging revealed co-activation and accumulation of the long noncoding RNAs (lncRNAs) $XACT$ and $XIST$ on active X chromosomes in both early human pre-implantation embryos and naive human embryonic stem cells. In these contexts, the $XIST$ RNA adopts an unusual, highly dispersed organization, which may explain why it does not trigger X chromosome inactivation at this stage. Functional studies in transgenic mouse cells show that $XACT$ influences $XIST$ accumulation in $cis$. Our findings therefore suggest a mechanism involving antagonistic activity of $XIST$ and $XACT$ in controlling X chromosome activity in early human embryos, and they highlight the contribution of rapidly evolving lncRNAs to species-specific developmental mechanisms.