We present optical photometry and spectroscopy of the broad-lined Type Ic supernova (SN Ic-BL) PTF10qts, which was discovered as part of the Palomar Transient Factory. The SN was located in a dwarf galaxy of magnitude r = 21.1 at a redshift z = 0.0907. We find that the R-band light curve is a poor proxy for bolometric data and use photometric and spectroscopic data to construct and constrain the bolometric light curve. The derived bolometric magnitude at maximum light is M$_bol$ = -18.51 ± 0.2 mag, comparable to that of SN 1998bw (M$_bol$ = -18.7 mag) which was associated with a gamma-ray burst (GRB). PTF10qts is one of the most luminous SNe Ic-BL observed without an accompanying GRB. We estimate the physical parameters of the explosion using data from our programme of follow-up observations, finding that it produced a larger mass of radioactive nickel compared to other SNe Ic-BL with similar inferred ejecta masses and kinetic energies. The progenitor of the event was likely an ̃20 M$_☉$ star.