We report our discovery of a nearby wide binary system, LP 714-37 AB. Phan-Bao et al. identified LP 714-37 as a mid-M dwarf during a cross-identification of the NLTT and DENIS catalogues. Our CCD images resolve the system into a binary with a projected angular separation of 1.8´´, or 33 AU, and low-resolution optical spectra give spectral types of M5.5 (LP 714-37A) and M7.5 (LP 714-37B). This makes LP 714-37 AB one of very few widely separated (separation >30 AU) very low-mass binary systems known in the field, and we discuss it in the context of the multiplicity properties of very low-mass stars and brown dwarfs.