Cesium lead bromide (CsPbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$) was recently introduced as a potentially high performance thin-film halide perovskite (HaP) material for optoelectronics, including photovoltaics, significantly more stable than MAPbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ (MA = CH$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$NH$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$+). Because of the importance of single crystals to study relevant material properties per se, crystals grown under conditions comparable to those used for preparing thin films, i.e., low-temperature solution-based growth, are needed. We show here two simple ways, antisolvent-vapor saturation or heating a solution containing retrograde soluble CsPbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$, to grow single crystals of CsPbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ from a precursor solution, treated with acetonitrile (MeCN) or methanol (MeOH). The precursor solutions are stable for at least several months. Millimeter-sized crystals are grown without crystal-seeding and can provide a 100% yield of CsPbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$ perovskite crystals, avoiding a CsBr-rich (or PbBr$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$-rich) composition, which is often present alongside the perovskite phase. Further growth is demonstrated to be possible with crystal seeding. The crystals are characterized in several ways, including first results of charge carrier lifetime (30 ns) and an upper-limit of the Urbach energy (19 meV). As the crystals are grown from a polar aprotic solvent (DMSO), which is similar to those used to grow hybrid organic-inorganic HaP crystals, this may allow growing mixed (organic and inorganic) monovalent cation HaP crystals.