I will introduce a new framework for locally adaptive Markov chain Monte Carlo (MCMC) samplers---Gibbs self tuning (GIST). With GIST, the tuning parameters of an MCMC algorithm are coupled with the MCMC state and sampled conditionally each iteration. I will sketch how several well-known Hamiltonian Monte Carlo samplers (multinomial, random, no U-turn, apogee-to-apogee) are instances. I will also introduce a novel sampler that locally adapts step size per leapfrog step in the no U-turn sampler (NUTS). The resulting sampler is able to traverse multiscale distributions that induce stiff Hamiltonian systems. I will conclude with a discussion of some preliminary results on locally adapting mass matrices. This is joint work with Tore Kleppe (Stavanger), Milo Marsden (Stanford), and Nawaf Bou-Rabee (Rutgers).