A plasma wakefield accelerator is a device that converts the energy of a relativistic particle beam into a large-amplitude wave in a plasma. The plasma wave, or wakefield, supports an enormous electric field that is used to accelerate a trailing particle beam. The plasma wakefield accelerator can therefore be used as a transformer, transferring energy from a high-charge, low-energy particle beam into a high-energy, low-charge particle beam. This technique may lead to a new generation of ultra-compact, high-energy particle accelerators. The past decade has seen enormous progress in the field of plasma wakefield acceleration with experimental demonstrations of the acceleration of electron beams by several gigaelectron-volts. The acceleration of positron beams in plasma is more challenging, but also necessary for the creation of a high-energy electron-positron collider. Part of the challenge is that the plasma responds asymmetrically to electrons and positrons, leading to increased disruption of the positron beam. One solution to this problem, first proposed over twenty years ago, is to use a hollow channel plasma which symmetrizes the response of the plasma to beams of positive and negative charge, making it possible to accelerate positrons in plasma without disruption. In this thesis, we describe the theory relevant to our experiment and derive new results when needed. We discuss the development and implementation of special optical devices used to create long plasma channels. We demonstrate for the first time the generation of meter-scale plasma channels and the accel Show Partial Abstract