Chilled water plants with multiple chillers are commonly used to provide cooling in large commercial buildings. Optimization offers a significant opportunity for improving the energy efficiency of such plants. Model based approaches used for control and optimization require accurate models, which can be difficult and/or expensive to obtain in practice due to large variations in equipment characteristics and operating conditions. In this paper, a model-free optimization strategy based on multivariate Extremum Seeking Control (ESC) with penalty terms is proposed for maximizing the energy efficiency of a chilled-water plant with parallel chillers. The feedback to ESC is the total power consumption of the plant consisting of chiller compressors, cooling tower fan, and condenser water pumps, in combination with penalty terms for input-saturation. The control inputs include the cooling tower fan airflow, condenser water flows and evaporator leaving chilledwater temperature setpoint. A band-pass filter array, instead of the high-pass filter in the standard ESC, is adopted to reduce the coupling among the input channels. The proposed strategy is evaluated with simulation study using a Modelica based dynamic simulation model of a chilledwater plant with two parallel chillers. Six cases are presented that demonstrate real-time optimization capability of ESC for this application.