We show that for an anomalous fluid carrying dissipationless chiral magnetic and/or vortical currents there is a frame in which a stationary obstacle experiences no drag, but energy and charge currents do not vanish, resembling superfluidity. However, unlike ordinary superfluid flow, the anomalous chiral currents do transport entropy in this frame. We show that the second law of thermodynamics completely determines the amounts of these anomalous non-dissipative currents in the "no-drag frame" as polynomials in temperature and chemical potential with known anomaly coefficients. These general results are illustrated and confirmed by a calculation in the chiral kinetic theory and quark-gluon plasma at high temperature.Introduction -The collective dynamics of a chiral (parity-violating) medium associated with quantum anomalies has become a subject of much attention recently. In particular, currents along the direction of an external magnetic field (chiral magnetic effect, or CME) discussed hypothetically earlier [1] have been recently proposed in Ref. [2,3] as a possible explanation of the charge dependent correlations observed in heavy-ion collisions and of negative magnetoresistance in a Diracsemimetal [4,5]. Currents in the direction of rotation axis (chiral vortical effect, or CVE) also discussed in astrophysical context before [6] have been (re)discovered in strong-coupling gauge-gravity calculations [7,8]. The generality of these effects and their connection to chiral anomaly have been demonstrated in Ref. [9,10] by applying the constraint of the second law of thermodynamics to the hydrodynamic equations for the anomalous chiral fluid.One of the manifestations of the anomalous nature of the CME and CVE currents is that these currents are dissipationless and do not lead to entropy production, in contrast, e.g., to the ordinary Ohmic current driven by electric field, but similar to the persistent superfluid currents. We wish to gain further understanding of the non-dissipative nature of the anomalous transport.How can one distinguish the anomalous CME/CVE currents from the uniform (shearless) inertial motion of the fluid as a whole in the same direction, which also does not generate entropy and carries energy and charge? To do this one needs to determine the "rest frame" of the "normal" component of the flow. This situation appears to be similar to the Landau's two-fluid picture of the superfluid [11]. The superfluid flow is also non-dissipative and carries energy (mass) and charge. Since it carries no entropy, one can define the rest frame of the normal component as the frame where the entropy flow vanishes. It is tempting to use the same criterion in the case of the anomalous CME/CVE flows. We shall show that, in general, this would not be correct, i.e., the CME/CVE currents do carry entropy.We propose that a natural way to define the "rest frame" of the normal component is to insert an impu-