We present studies of strong coupling in single-photon photoassociation of cesium dimers using an optical dipole trap. A thermodynamic model of the trap depletion dynamics is employed to extract absolute rate coefficents. From the dependence of the rate coefficient on the photoassociation laser intensity, we observe saturation of the photoassociation scattering probability at the unitarity limit in quantitative agreement with the theoretical model by Bohn and Julienne [1]. Also the corresponding power broadening of the resonance width is measured. We could not observe an intensity dependent light shift in contrast to findings for lithium and rubidium, which is attributed to the absence of a p or d-wave shape resonance in cesium.PACS numbers: 34.50. Rk,32.80.Pj Ultracold thermal and quantum degenerate atomic ensembles have allowed to investigate powerful coupling schemes between continuum scattering states of two atoms and bound molecular states of the corresponding dimer. Both photoassociation light [2,3] or magnetic field sweeps across Feshbach resonances [4,5,6] have lead to the formation of ultracold molecules. Three-body recombination of fermionic atoms near a Feshbach resonance has finally lead to the creation of molecular Bose Einstein condensates [7,8,9]. Recently, molecular photoassociation has been performed using a two-photon Raman process in a two-atom Mott insulator phase [10], which may prove to be a route to a molecular Mott insulator and, subsequently, an alternative way to a molecular BEC [11]. In contrast to this, the successful formation of ultacold molecular ensembles in the absolute rovibrational ground state, which is important if one wants to study molecular collisions and reactions over long interaction times, is still at large. Future routes for the production of absolute ground state molecules from a pair of atoms will certainly involve Raman type coupling schemes [12,13,14]. A very interesting approach to transfer highly vibrationally excited molecules into the vibrational ground state proposes the application of optimally controlled femtosecond laser pulses [15].In order to understand the regime of strong coupling in photoassociation, which is important for both continuous and femtosecond Raman processes, we report in this Rapid Communication investigations of saturation effects in the first photoassociation step from the two-atom continuum to an excited molecular level. This is also the determining step in the overall molecule formation rate [16]. Using an ultracold ensemble of cesium atoms trapped in a quasi-electrostatic optical trap [17] we are able to employ trap loss measurements to extract absolute photoassociation rate coefficients [18], from which the dependence of the rate coefficient on the photoassociation laser intensity is derived.