An enumerably infinite graph G is hypohamiltonian, if it has no two-way infinite hamiltonian path, but every vertex deleted subgraph G-v has such a path. Thomassen gives examples of infinite hypohamiltonian graphs. Each of these graphs has a vertex of infinite degree. An infinite graph is called locally finite, if every vertex has finite degree. Thomassen raised the question, if there exist infinite hypohamiltonian graphs that are locally finite. In this paper we give an example of an infinite locally finite hypohamiltonian graph, which is planar and has vertices of degree three or four, only. Moreover, we show that there are infinitely many infinite locally finite hypohamiltonian graphs.