We detect luminous emission from HCN, HCO+ and HNC 1--0 in the QSO ULIRG Mrk~231 with the IRAM Plateau de Bure Interferometer at 1.55 by 1.28 resolution. All three lines show broad line wings - which are particularly prominent for HCN. Velocities are found to be similar (750 km/s) to those found for CO 1-0. This is the first time bright HCN, HCO+ and HNC emission has been detected in a large-scale galactic outflow. We find that both the blue- and red-shifted line wings are spatially extended by at least 0.75 (700 pc) in a north-south direction. The line wings are brighter (relative to the line center intensity) in HCN than in CO 1-0 and line ratios suggest that the molecular outflow consists of dense (n>10E4 cmE-3) and clumpy gas with a high HCN abundance X(HCN)>10E-8. These properties are consistent with the molecular gas being compressed and fragmented by shocks in the outflow. Alternatively, HCN is instead pumped by mid-IR continuum, but we propose that this effect is not strong for the spatially extended outflowing gas. In addition, we find that the rotation of the main disk, in east-west direction, is also evident in the HCN, HCO+ and HNC line emission. An unexpectedly bright HC3N 10-9 line is detected inside the central 400 pc of Mrk231. This HC3N emission may emerge from a shielded, dust-enshrouded region within the inner 40-50 pc where the gas is heated to high temperatures (200 - 300 K) by the AGN.
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