With the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we have discovered in M4 (NGC 6121, C 1620-264) the first extensive sequence of cooling white dwarfs seen in a globular cluster. Adopting a distance modulus of (m-M)_V = 12.65 and a reddening of E(B-V) = 0.37, we show that the sequence, which extends over 9 < M_U < 13, is comprised of white dwarfs of mass sim 0.5 M_{odot}. The total mass loss from the present turnoff to the white dwarf sequence is 0.31 M_{odot} and the intrinsic dispersion in the mean mass appears to be < 0.05 M_{odot}. Both the location of the white dwarf cooling sequence in the cluster color-magnitude diagram and the cumulative luminosity function attest to the basic correctness and completeness of the physics in theoretical models for the upper three magnitudes of the observed white dwarf cooling sequence. To test the theory in globular clusters at cooling ages beyond sim 3 times 10^8 years will require deeper and more complete data.
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