A graph G is m-choosable with impropriety d, or simply
(m, d)*-choosable, if, for every list
assignment L, where [mid ]L(v)[mid ][ges ]m
for every v∈V(G), there exists an L-colouring of
G such that each vertex of G has at most d
neighbours coloured with the same colour as
itself. We prove a Grötzsch-type theorem for list colourings with impropriety one, that is,
the (3, 1)*-choosability for triangle-free planar graphs; in the proof the method of
extending a precolouring of a 4- or 5-cycle is used.