First Observation and Dalitz Analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mi>η</mml:mi><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>Decay

Using 9.0 fb(-1) of integrated luminosity in e(+)e(-) collisions near the Upsilon(4S) mass collected with the CLEO II.V detector we report the first observation of the decay D0-->K(0)(S)etapi(0). We measure the ratio of branching fractions, BR(D0-->K(0)(S)etapi(0))BR / (D0-->K(0)(S)pi(0))=0.46+/-0.07+/-0.06. We perform a Dalitz analysis of 155 selected D0-->K(0)(S)etapi(0) candidates and find leading contributions from a(0)(980)K(0)(S) and K(*)(892)eta intermediate states.