We present the results of a new sensitive survey of neutral hydrogen above and below the Galactic Center with the Green Bank Telescope . The observations extend up to Galactic latitude \mid b \mid < 10 { { } ^ { \circ } } with an effective angular resolution of 9.5 ^ { \prime } and an average rms brightness temperature noise of 40 mK in a 1 km s ^ { -1 } channel . The survey reveals the existence of a population of anomalous high-velocity clouds extending up to heights of about 1.5 kpc from the Galactic Plane and showing no signature of Galactic rotation . These clouds have local standard of rest velocities \mid { V _ { \mathrm { LSR } } } \mid \lesssim 360 km s ^ { -1 } and , assuming a Galactic Center origin , they have sizes of a few tens of parsecs and neutral hydrogen masses spanning 10 - 10 ^ { 5 } { M } _ { \odot } . Accounting for selection effects , the cloud population is symmetric in longitude , latitude , and V _ { \mathrm { LSR } } . We model the cloud kinematics in terms of an outflow expanding from the Galactic Center and find the population consistent with being material moving with radial velocity { V _ { \mathrm { w } } } \simeq 330 { km s ^ { -1 } } distributed throughout a bi-cone with opening angle \alpha > 140 { { } ^ { \circ } } . This simple model implies an outflow luminosity L _ { \mathrm { w } } > 3 \times 10 ^ { 40 } erg s ^ { -1 } over the past 10 Myr , consistent with star formation feedback in the inner region of the Milky Way , with a cold gas mass-loss rate \lesssim 0.1 { M _ { \odot } yr } ^ { -1 } . These clouds may represent the cold gas component accelerated in the nuclear wind driven by our Galaxy , although some of the derived properties challenge current theoretical models of the entrainment process .