Let \({\mathcal L}_n\), \(n\geq 2\), be the filiform Lie algebra, namely \({\mathcal L}_n= \langle X_1,\dots, X_{n+1}\rangle_{\mathbb{R}}\) with non-trivial bracket relations \([X_{n+1}, X_j]= X_{j-1}\) \((2\leq j\leq n)\). Let \(L_n= \exp({\mathcal L}_n)\) be the associated connected and simply connected nilpotent Lie group. A discrete subgroup \(\Gamma\) of a Lie group \(G\) such that the homogeneous space \(G/\Gamma\) is compact is called a uniform subgroup of \(G\). \textit{A. I. Mal'tsev} [Izv. Akad. Nauk SSSR, Ser. Mat. 13, 9--32 (1949), English translation in Am. Math. Soc. Transl. 1951, No. 39, 33 pp. (1951; Zbl 0034.01701)] showed that a simply connected nilpotent Lie group admits a uniform subgroup if and only if its Lie algebra has a basis with rational structure constants. So, it follows that every filiform group \(L_n\) admits a uniform subgroup. The paper determines up to isomorphism all uniform subgroups of \(L_n\). As examples, the author also describes explicitly the uniform subgroups of \(L_3\) and \(L_4\).