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We present the publicly available, open source code UCLCHEMCMC, designed to estimate physical parameters of an observed cloud of gas by combining Monte Carlo Markov Chain (MCMC) sampling with chemical and radiative transfer modeling. When given the observed values of different emission lines, UCLCHEMCMC runs a Bayesian parameter inference, using a MCMC algorithm to sample the likelihood and produce an estimate of the posterior probability distribution of the parameters. UCLCHEMCMC takes a full forward modeling approach, generating model observables from the physical parameters via chemical and radiative transfer modeling. While running UCLCHEMCMC, the created chemical models and radiative transfer code results are stored in an SQL database, preventing redundant model calculations in future inferences. This means that the more UCLCHEMCMC is used, the more efficient it becomes. Using UCLCHEM and RADEX, the increase of efficiency is nearly two orders of magnitude, going from 5185.33 \pm 1041.96 s for ten walkers to take one thousand steps when the database is empty, to 68.89 \pm 45.39 s when nearly all models requested are in the database. In order to demonstrate its usefulness we provide an example inference of UCLCHEMCMC to estimate the physical parameters of mock data, and perform two inferences on the well studied prestellar core, L1544, one of which show that it is important to consider the substructures of an object when determining which emission lines to use.