Cepheidsplayakeyroleinastronomyasstandardcandlesformeasuringintergalacticdistances.TheirdistanceisusuallyinferredfromthePeriod-Luminosityrelationship , calibratedusingthesemi-empiricalBaade-Wesselinkmethod.Usingthismethod , thedistanceisknowntoamultiplicativefactor , calledtheprojectionfactor.Presently , thisfactoriscomputedusingnumericalmodels-ithashithertoneverbeenmeasureddirectly.BasedonournewinterferometricmeasurementsobtainedwiththeCHARAArrayandthealreadypublishedparallax , wepresentageometricalmeasurementoftheprojectionfactorofaCepheid , $ δ $ ~Cep .Thevaluewedetermined , p = 1.27 \pm 0.06 , confirmsthegenerallyadoptedvalueof p = 1.36 within1.5sigmas.Ourvalueisinlinewithrecenttheoreticalpredictionsof .