Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. Here, we propose a chiral spin-orbital liquid as a stable phase of a realistic model for heavy-element double perovskites. This spin liquid state has Majorana fermion excitations with a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. We show that the nodal lines are topological defects of a non-Abelian Berry connection and that the system exhibits dispersing surface states. We discuss some experimental signatures of this state and compare them with properties of the spin liquid candidate Ba2YMoO6.1171Brazilian agency FAPESPBrazilian agency CNPqFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)