We present high resolution HST ultraviolet spectroscopy of NGC 3242 , the only planetary nebula with a measured abundance of ^ { 3 } He . The Space Telescope Imaging Spectrograph ( STIS ) has been used to observe the C iii multiplet near \lambda 1908 Å . The presence of ^ { 12 } C and ^ { 13 } C lines at these wavelengths allows a direct estimate of the carbon isotopic ratio in the ionized gas of the nebula . We have detected the ^ { 12 } C doublet and obtained an upper limit on the ^ { 13 } C \lambda 1909.6 Å line , resulting in a carbon isotopic ratio ^ { 12 } C/ ^ { 13 } C > 38 , in agreement with standard stellar models . The lack of the ^ { 13 } C line and the presence of the ^ { 3 } He line in the spectrum indicate that the progenitor star did not undergo a phase of deep mixing during the last stages of its evolution . The significance of this result for studies of stellar nucleosynthesis and Galactic chemical evolution is discussed .