  We measure the branching ratio of the purely leptonic decay of the D+ meson
with unprecedented precision as B(D+ -> mu+ nu) = (3.82 +/- 0.32 +/-
0.09)x10^(-4), using 818/pb of data taken on the psi(3770) resonance with the
CLEO-c detector at the CESR collider. We use this determination to derive a
value for the pseudoscalar decay constant fD+, combining with measurements of
the D+ lifetime and assuming |Vcd| = |Vus|. We find fD+ = (205.8 +/- 8.5 +/-
2.5) MeV. The decay rate asymmetry [B(D+ -> mu+ nu)-B(D- -> mu- nu)]/[B(D+ ->
mu+ nu)+B(D- -> mu- nu)] = 0.08 +/- 0.08, consistent with no CP violation. We
also set 90% confidence level upper limits on B(D+ -> tau+ nu) < 1.2x10^(-3)
and B(D+ -> e+ nu) < 8.8x10^(-6).
