We have analyzed spectra of the Galactic black hole GX 339 - 4 obtained through simultaneous 76 ksec XMM-Newton /EPIC-pn and 10 ksec RXTE observations during a bright phase of its 2002–2003 outburst . An extremely skewed , relativistic Fe K \alpha emission line and ionized disk reflection spectrum are revealed in these spectra . Self-consistent models for the Fe K \alpha emission line profile and disk reflection spectrum rule-out an inner disk radius compatible with a Schwarzschild black hole at more than the 8 \sigma level of confidence . The best-fit inner disk radius of 2 - 3 ~ { } r _ { g } suggests that GX 339 - 4 harbors a black hole with a \geq 0.8 - 0.9 ( where r _ { g } = GM / c ^ { 2 } and a = cJ / GM ^ { 2 } , and assuming that reflection in the plunging region is relatively small ) . This confirms indications for black hole spin based on a Chandra spectrum obtained later in the outburst . The emission line and reflection spectrum also rule-out a standard power-law disk emissivity in GX 339 - 4 ; a broken power-law form with enhanced emissivity inside \sim 6 ~ { } r _ { g } gives improved fits at more than the 8 \sigma level of confidence . The extreme red wing of the line and steep emissivity require a centrally–concentrated source of hard X-rays which can strongly illuminate the inner disk . Hard X-ray emission from the base of a jet — enhanced by gravitational light bending effects — could create the concentrated hard X-ray emission ; this process may be related to magnetic connections between the black hole and the inner disk . We discuss these results within the context of recent results from analyses of XTE J1650 - 500 and MCG–6–30–15 , and models for the inner accretion flow environment around black holes .