The proton resonant firehose instability may arise in collisionless plasmas in which the proton velocity distribution is approximately bi-Maxwellian with T∥p/T⊥p > 1, where ⊥ and ∥ denote directions relative to the background magnetic field B○. Linear theory and one-dimensional simulations predict that enhanced field fluctuations from the proton resonant firehose instability impose a constraint on proton temperature anisotropies of the form 1 - T⊥p/T∥p = Sp/¿∥pαp where ¿∥p ≡ 8πnpkBT∥p/B○2, and the fitting parameters Sp ~ 1 and αp ≃ 0.7. Observations from the Wind spacecraft are reported here. These measurements show for the first time with a comprehensive plasma and magnetic field data set that this constraint is statistically satisfied in the solar wind near 1 AU, with best-fit values of Sp = 1.21 ¿ 0.26 and αp = 0.76 ¿ 0.14.