We present a measurement of the electron charge asymmetry in $p\overline{p}\ensuremath{\rightarrow}W+X\ensuremath{\rightarrow}e\ensuremath{\nu}+X$ events at a center of mass energy of 1.96 TeV using $0.75\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected with the D0 detector at the Fermilab Tevatron Collider. The asymmetry is measured as a function of the electron transverse momentum and pseudorapidity in the interval ($\ensuremath{-}3.2$, 3.2) and is compared with expectations from next-to-leading order calculations in perturbative quantum chromodynamics. These measurements will allow more accurate determinations of the proton parton distribution functions.