This paper uses the Hotelling-Downs spatial model of electoral competition between candidates to explore competition between political parties. Two parties choose platforms in a unidimensional policy space, and then in a continuum of constituencies with different median voters candidates from the two parties compete in first-past-the-post elections. Departing from party platform is costly enough that candidates do not take the median voter?s preferred position in each constituency. In equilibrium, parties acting in their candidates? best interests differentiate?when one party locates right of center, the other prefers to locate strictly left of center to carve out a ?home turf,? consituencies that can be won with little to no deviation from party platform. Hence, Downsian competition that pulls candidates together pushes parties apart. Decreasing ?campaign costs? increases party differentiation as the leftist party must move further from the rightist party to carve out its home turf. For a range of costs, parties take more extreme positions than their most extreme candidates. For small costs, parties are too extreme to maximize voter welfare, whereas for large costs they are not extreme enough.