  We present the first results of the Fermilab Muon g-2 Experiment for the
positive muon magnetic anomaly $a_\mu \equiv (g_\mu-2)/2$. The anomaly is
determined from the precision measurements of two angular frequencies.
Intensity variation of high-energy positrons from muon decays directly encodes
the difference frequency $\omega_a$ between the spin-precession and cyclotron
frequencies for polarized muons in a magnetic storage ring. The storage ring
magnetic field is measured using nuclear magnetic resonance probes calibrated
in terms of the equivalent proton spin precession frequency
${\tilde{\omega}'^{}_p}$ in a spherical water sample at 34.7$^{\circ}$C. The
ratio $\omega_a / {\tilde{\omega}'^{}_p}$, together with known fundamental
constants, determines $a_\mu({\rm FNAL}) = 116\,592\,040(54)\times 10^{-11}$
(0.46\,ppm). The result is 3.3 standard deviations greater than the standard
model prediction and is in excellent agreement with the previous Brookhaven
National Laboratory (BNL) E821 measurement. After combination with previous
measurements of both $\mu^+$ and $\mu^-$, the new experimental average of
$a_\mu({\rm Exp}) = 116\,592\,061(41)\times 10^{-11}$ (0.35\,ppm) increases the
tension between experiment and theory to 4.2 standard deviations
