Continuous and pulsed quantum Zeno effects were observed using a 87Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(R), were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005 omega(R).