We present Spitzer Space Telescope infrared photometry of a primary transit of the hot Neptune GJ 436b . The observations were obtained using the 8 \mu m band of the InfraRed Array Camera ( IRAC ) . The high accuracy of the transit data and the weak limb-darkening in the 8 \mu m IRAC band allow us to derive ( assuming M = 0.44 \pm 0.04 M _ { \odot } for the primary ) a precise value for the planetary radius ( 4.19 ^ { +0.21 } _ { -0.16 } R _ { \oplus } ) , the stellar radius ( 0.463 ^ { +0.022 } _ { -0.017 } R _ { \odot } ) , the orbital inclination ( 85.90 ^ { \circ } ^ { +0.19 ^ { \circ } } _ { -0.18 ^ { \circ } } ) and transit timing ( 2454280.78186 ^ { +0.00015 } _ { -0.00008 } HJD ) . Assuming current planet models , an internal structure similar to that of Neptune with a small H/He envelope is necessary to account for the measured radius of GJ 436b .