E865 at the Brookhaven National Laboratory AGS collected about 70 000 Ke3+ events to measure the Ke3+ branching ratio relative to the observed K+→π+π0, K+→π0μ+ν, and K+→π+π0π0 decays. The π0 in all the decays was detected using the e+e- pair from π0→e+e-γ decay and no photons were required. Using the 2002 Particle Data Group branching ratios for the normalization decays, we obtain BR(Ke3(γ)+)=(5.13±0.02stat±0.09syst±0.04norm)%, where Ke3(γ)+ includes the effect of virtual and real photons. This result is ≈2.3σ higher than the current Particle Data Group value. Implications for the Vus element of the CKM matrix, and the matrix’s unitarity are discussed.