Isothermal amplification methods for detection of DNA and RNA targets have expanded significantly in recent years, promising a new wave of simple and rapid molecular diagnostics. Current isothermal methods result in the generation of short fragments (<150 base pairs) or highly branched long DNA products. Here we report the amplification of discrete target fragments of several kilobases at 37 °C from both double- and single-stranded circular template DNA using specific primer pairs. In contrast to existing methods, this amplification requires only the single-stranded DNA-binding protein gp32 from bacteriophage T4 and a strand-displacing DNA polymerase. In addition to the discrete amplicon products, this method also produces higher molecular weight products consisting of multiple repeated copies of the amplicon and template DNA. We demonstrate that two features of gp32 enable this amplification: a facilitation of primer strand invasion into double-stranded DNA, and a suppression of non-homologous primer annealing and nonspecific amplification. The ability presented here to produce long, discrete DNA products in an isothermal reaction extends the scope of isothermal amplification to enable more useful applications of these promising methods.