The time-dependent response of the tropical atmosphere to a fixed, localized sea surface temperature (SST) anomaly is explored using a highly simplified nonlinear shallow water numerical model. The work builds on that by Webster <1972> and Gill <1980>. The present model has three layers and is formulated on an equatorial beta plane in an atmosphere initially in radiative-convective equilibrium. Observations suggest that the tropical atmosphere is only marginally unstable to moist convection. Accordingly, the convective parameterization in the model assumes that clouds consume the convective available potential energy at approximately the same rate as large-scale processes generate it. The convective parameterization allows for both shallow nonprecipitating and deep precipitating clouds. The convection scheme allows the shallow convection to condition the atmosphere for further deep convection, which is an important factor controlling deep convection in the tropics. The model calculations show that shallow convection moistens the middle troposphere, providing favorable conditions for the development of deep convection. In contrast, radiative cooling and drying of the middle troposphere act to suppress deep convection. In the model, these competing processes modulate the deep convection over the localized SST anomaly with a period of about 30 days. The convective heating also excites large-scale, equatorially trapped normal modes. The response ranges from a steady state flow similar to that by Gill to a periodic generation of Rossby-Kelvin wave couplets and finally to a transition to chaotic behavior depending on the strength of the forcing.