We measure the two-point correlation function \xi ( r _ { p } , \pi ) in a sample of 2219 galaxies between z = 0.7 - 1.35 to a magnitude limit of R _ { AB } = 24.1 from the first season of the DEEP2 Galaxy Redshift Survey . From \xi ( r _ { p } , \pi ) we recover the real-space correlation function , \xi ( r ) , which we find can be approximated within the errors by a power-law , \xi ( r ) = ( r / r _ { 0 } ) ^ { - \gamma } , on scales \sim 0.1 - 10 h ^ { -1 } Mpc . In a sample with an effective redshift of z _ { eff } = 0.82 , for a \Lambda CDM cosmology we find r _ { 0 } = 3.53 \pm 0.81 h ^ { -1 } Mpc ( comoving ) and \gamma = 1.66 \pm 0.12 , while in a higher-redshift sample with z _ { eff } = 1.14 we find r _ { 0 } = 3.12 \pm 0.72 h ^ { -1 } Mpc and \gamma = 1.66 \pm 0.12 . These errors are estimated from mock galaxy catalogs and are dominated by the cosmic variance present in the current data sample . We find that red , absorption-dominated , passively-evolving galaxies have a larger clustering scale length , r _ { 0 } , than blue , emission-line , actively star-forming galaxies . Intrinsically brighter galaxies also cluster more strongly than fainter galaxies at z \simeq 1 . Our results imply that the DEEP2 galaxies have an effective bias b = 0.96 \pm 0.13 if \sigma _ { 8 { DM } } = 1 today or b = 1.19 \pm 0.16 if \sigma _ { 8 { DM } } = 0.8 today . This bias is lower than what is predicted by semi-analytic simulations at z \simeq 1 , which may be the result of our R -band target selection . We discuss possible evolutionary effects within our survey volume , and we compare our results with galaxy clustering studies at other redshifts , noting that our star-forming sample at z \simeq 1 has very similar selection criteria as the Lyman-break galaxies at z \simeq 3 and that our red , absorption-line sample displays a clustering strength comparable to the expected clustering of the Lyman-break galaxy descendants at z \simeq 1 . Our results demonstrate that galaxy clustering properties as a function of color , spectral type and luminosity seen in the local Universe were largely in place by z \simeq 1 .