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We present an extensive $\textit{Hubble Space Telescope}$ ($\textit{HST}$)rest-frame ultraviolet (UV) imaging study of the locations of Type Isuperluminous supernovae (SLSNe) within their host galaxies. The sampleincludes 65 SLSNe with detected host galaxies in the redshift range $z\approx0.05-2$. Using precise astrometric matching with SN images, we determine thedistributions of physical and host-normalized offsets relative to the hostcenters, as well as the fractional flux distribution relative to the underlyingUV light distribution. We find that the host-normalized offsets of SLSNeroughly track an exponential disk profile, but exhibit an overabundance ofsources with large offsets of $1.5-4$ times their host half-light radius. TheSLSNe normalized offsets are systematically larger than those of long gamma-raybursts (LGRBs), and even Type Ib/c and II SNe. Furthermore, we find that about40\% of all SLSNe occur in the dimmest regions of their host galaxies(fractional flux of 0), in stark contrast to LGRBs and Type Ib/c and II SNe. Wedo not detect any significant trends in the locations of SLSNe as a function ofredshift, or as a function of explosion and magnetar engine parameters inferredfrom modeling of their optical lights curves. The significant difference inSLSN locations compared to LGRBs (and normal core-collapse SNe) suggests thatat least some of their progenitors follow a different evolutionary path. Wespeculate that SLSNe arise from massive runaway stars from disrupted binarysystems, with velocities of $\sim 10^2$ km s$^{-1}$.

An Extensive $\textit{Hubble Space Telescope}$ Study of the Offset and Host Light Distributions of Type I Superluminous Supernovae