Plasma-based accelerators have been proposed for the next generation of compact accelerators because of the huge electric fields they can support. However, it has been difficult to use them efficiently for applications because they produce poor quality particle beams with large energy spreads. Here, we demonstrate a dramatic enhancement in the quality of electron beams produced in laser-plasma interaction: an ultrashort laser pulse drives a plasma bubble which traps and accelerates plasma electrons to a single energy. This produces an extremely collimated and quasi-monoenergetic electron beam with a high charge of 0.5 nanocoulomb at energy 170 ± 20 MeV.