We search for color singlet technirho and technipion production in ppbar collisions at sqrt s = 1.8 TeV recorded with the Collider Detector at Fermilab. These exotic technimesons are present in a model of walking technicolor. The signatures studied are lepton plus two jets and multijet final states. No excess of events is seen in either final state. We set an upper limit on the technirho production cross section and exclude a region in the technipion mass versus technirho mass plane at the 95% confidence level.