  Let $ \mathfrak{g} $ be an untwisted affine Kac-Moody algebra over the field
$ K \, $, and let $ U_q(\mathfrak{g}) $ be the associated quantum enveloping
algebra; let $ \mathfrak{U}_q(g) $ be the Lusztig's integer form of $
U_q(\mathfrak{g}) \, $, generated by $ q $-divided powers of Chevalley
generators over a suitable subring $ R $ of $ K(q) \, $. We prove a
Poincar\'e-Birkhoff-Witt like theorem for $ \mathfrak{U}_q(\mathfrak{g}) \, $,
yielding a basis over $ R $ made of ordered products of $ q $-divided powers of
suitable quantum root vectors.
