Functions for simulating Markov chains using the Barker proposal to compute Markov chain Monte Carlo (MCMC) estimates of expectations with respect to a target distribution on a real-valued vector space. The Barker proposal, described in Livingstone and Zanella (2022) <doi:10.1111/rssb.12482>, is a gradient-based MCMC algorithm inspired by the Barker accept-reject rule. It combines the robustness of simpler MCMC schemes, such as random-walk Metropolis, with the efficiency of gradient-based methods, such as the Metropolis adjusted Langevin algorithm. The key function provided by the package is sample_chain(), which allows sampling a Markov chain with a specified target distribution as its stationary distribution. The chain is sampled by generating proposals and accepting or rejecting them using a Metropolis-Hasting acceptance rule. During an initial warm-up stage, the parameters of the proposal distribution can be adapted, with adapters available to both: tune the scale of the proposals by coercing the average acceptance rate to a target value; tune the shape of the proposals to match covariance estimates under the target distribution. As well as the default Barker proposal, the package also provides implementations of alternative proposal distributions, such as (Gaussian) random walk and Langevin proposals. Optionally, if 'BridgeStan's R interface <https://roualdes.github.io/bridgestan/latest/languages/r.html>, available on GitHub <https://github.com/roualdes/bridgestan>, is installed, then 'BridgeStan' can be used to specify the target distribution to sample from.