We present an algorithm for the tracking of a variable number of 3D persons in a multi-camera setting with partial field-of-view overlap. The multi-object tracking problem is posed in a Bayesian framework and relies on a joint multi-object state space with individual object states defined in the 3D world. The Reversible Jump Markov Chain Monte Carlo (RJ-MCMC) method is used to efficiently search the state-space and recursively estimate the multi-object configuration. The paper presents several contributions: i) the use and extension of several key features for efficient and reliable tracking (e.g. the use of the MCMC framework for multiple camera MOT; the use of powerful human detector outputs in the MCMC proposals to automatically initialize/update object tracks); ii) the definition of appropriate prior on the object state, to take into account the effects of 2D image measurement uncertainties on the 3D object state estimation due to depth effects; iii) a simple rectification method aligning people 3D standing direction with 2D image vertical axis, allowing to obtain better object measurements relying on rectangular boxes and integral images; iv) representing objects with multiple reference color histograms, to account for variability in color measurement due to changes in pose, lighting, and importantly multiple camera view points. Experimental results on challenging real-world tracking sequences and situations demonstrate the efficiency of our approach.