Long-read sequencing technologies have the potential to produce gold-standard de novo genome assemblies, but fully exploiting error-prone reads to resolve repeats remains a challenge. Aggressive approaches to repeat resolution often produce misassemblies, and conservative approaches lead to unnecessary fragmentation. We present HINGE, an assembler that seeks to achieve optimal repeat resolution by distinguishing repeats that can be resolved given the data from those that cannot. This is accomplished by adding "hinges" to reads for constructing an overlap graph where only unresolvable repeats are merged. As a result, HINGE combines the error resilience of overlap-based assemblers with repeat-resolution capabilities of de Bruijn graph assemblers. HINGE was evaluated on the long-read bacterial data sets from the NCTC project. HINGE produces more finished assemblies than Miniasm and the manual pipeline of NCTC based on the HGAP assembler and Circlator. HINGE also allows us to identify 40 data sets where unresolvable repeats prevent the reliable construction of a unique finished assembly. In these cases, HINGE outputs a visually interpretable assembly graph that encodes all possible finished assemblies consistent with the reads, while other approaches such as the NCTC pipeline and FALCON either fragment the assembly or resolve the ambiguity arbitrarily.