AMOEBA (Automated Molecular Excitation Bayesian line-fitting Algorithm) employs a Bayesian approach to Gaussian decomposition, resulting in an objective and statistically robust identification of individual clouds along the line-of-sight. It uses the Python implementation of Goodman & Weare's Affine Invariant Markov chain Monte Carlo (MCMC) Ensemble sampler emcee (ascl:1303.002) to sample the posterior probability distribution and numerically evaluate the integrals required to compute the Bayes Factor. Amoeba takes as input a set of OH optical depth spectra and a set of expected brightness temperature spectra that are obtained by measuring the brightness temperature towards the bright background continuum source (the "on-source" observations), and in a pattern surrounding the continuum source (the "off-source" observations). Amoeba can also take as input a set of OH optical depth spectra only, and also allows input of an arbitrary number of spectra to be fit simultaneously.