We report results from an experiment designed to test the conserved vector current (CVC) hypothesis by measuring the shape of the β-decay spectrum for the allowed 0+ → 1+ ground state decay of 14O. Measurements of the spectrum intensity were obtained with a superconducting beta spectrometer and will be reported for positron kinetic energies ranging from 1.9 to 4.0 MeV. After dividing out phase space, Coulomb, and other correction factors, the resulting shape function has a negative slope of several percent per MeV. We define a parameter a′ , which is essentially a measure of the average slope of the shape function over the energy range of the measurements, and determine its value to be a′ = −0.0290 ± 0.0008 (stat.) ±0.0006 (syst.). The measured slope parameter is in good agreement with predictions from shell model calculations that respect CVC.