We present an analysis of the 101 { \thinspace ks } , 2007 Suzaku spectrum of the LINER galaxy NGC 1052 . The 0.5 - 10 { \thinspace keV } continuum is well-modeled by a power-law modified by Galactic and intrinsic absorption , and it exhibits a soft , thermal emission component below 1 { \thinspace keV } . Both a narrow core and a broader component of Fe K \alpha emission centered at 6.4 { \thinspace keV } are robustly detected . While the narrow line is consistent with an origin in material distant from the black hole , the broad line is best fit empirically by a model that describes fluorescent emission from the inner accretion disk around a rapidly rotating black hole . We find no evidence in this observation for Comptonized reflection of the hard X-ray source by the disk above 10 { \thinspace keV } , however , which casts doubt on the hypothesis that the broad iron line originates in the inner regions of a standard accretion disk . We explore other possible scenarios for producing this spectral feature and conclude that the high equivalent width ( EW \sim 185 { \thinspace keV } ) and full-width-half-maximum velocity of the broad iron line ( v \geq 0.37 c ) necessitate an origin within d \sim 8 r _ { g } of the hard X-ray source . Based on the confirmed presence of a strong radio jet in this galaxy nucleus , the broad iron line may be produced in dense plasma near the base of the jet , implying that emission mechanisms in the centralmost portions of active galactic nuclei are more complex than previously thought .