The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius r(d) and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium mu d is the exotic atom formed by a deuteron and a negative muon mu-. We measured three 2S-2P transitions in md and obtain r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5 sigma smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The md value is also 3.5 sigma smaller than the rd value from electronic deuterium spectroscopy. The smaller rd, when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle.