The 19.37-eV helium scattering resonance profile has been measured with an instrumental width less than the natural width and much less than that attained in any previously published study. The electron beam was produced by photoionization and scattered from a He beam from a supersonic nozzle. The instrumental width, including residual Doppler effects, was routinely around 5 meV and the current was 5)& 10 " A. The profile was measured at 22', 90', and 135' scattering angles. From the 90 and 135 data the sand p-wave. phase shifts were found to be 1.813~0.017 and 0.309~0.013 radians, respectively. The natural width I' of the resonance was inferred by two methods: nonlinear least-squares fitting, and use of the integral of the differential cross section over the resonance, Both methods yield 11. 0+0.5 meV, if it is assumed that there is no instrumental background in the scattered electron signal. Experimental evidence indicates that any such instrumental background must be less than 15% of the total signal, and is probably less than 5%. If an extreme. allowance is made for the larger figure, a I' as high as 13 meV could be possible.