We propose a six-year research and development program to develop the hardware needed for ionization cooling, and demonstrate the feasibility of using the ionization cooling technique to produce cooled beams of positive and negative muons for a muon collider. We propose to design and prototype critical sections of the muon ionization cooling channel. These sections would be tested by measuring their performance when exposed to single incoming muons with momenta in the range 100 -- 300 MeV/c. The phase-space volume occupied by the population of muons upstream and downstream of the cooling sections would be measured sufficiently well to enable cooling to be demonstrated, the calculations used to design the cooling system to be tested, and optimization of the cooling hardware to be studied. Posted muc0001.ps to WWW URL http://www-mucool.fnal.gov/mcnotes/muc0001.ps Posted by Buckley