How do I make SMOOTH pureed chicken for baby food?

I put very small chunks of cold cooked chicken in a food processor until it looked like small grains of cous cous (I couldn't get it any more 'powdery' than that). Then I added cold chicken stock. The consistency was very stringy, like mushy chicken salad? I need it to be smooth like mayonaise (like how it is in Gerber meats jars) as my daughter hates anything with texture. What did I do wrong? Help!