Using a crossed electron-molecular-beam apparatus, absolute elastic cross sections for electron scattering from the CF3 molecule were measured. Differential cross sections were determined for incident electron energies in the range 7-50 eV and over an angular range of 20-135. Integral cross sections are subsequently derived from those data. The present measurements are compared to theoretical predictions using an extended independent atom model approach, and with earlier R-matrix and Schwinger Multichannel results. Agreement with theory is generally good at energies above 20 eV, but for 20 eV and below the measured cross sections are significantly larger than those predicted by all theories.