In this paper, we show the existence of a weak solution for a fractional sub-Laplace equation involving a term with the critical Sobolev exponent, namely, \((-\varDelta _\mathbb {H})^su - \lambda u = |u|^{Q^*_s -2}u \text { in } \varOmega , u= 0 \text { in } \mathbb {H}^N \setminus \varOmega , \) where \(\varOmega \subseteq \mathbb {H}^N\) is bounded and has continuous boundary, \((-\varDelta _\mathbb {H})^s\) is the horizontal fractional Laplacian, \(s \in (0,1), \lambda > 0,\) and \(Q^*_s=\frac{2Q}{Q-2s}\) is the Sobolev critical exponent. This problem is motivated by the celebrated Brezis-Nirenberg problem [10].
