  We present spectroscopic measurements of the [OIII] emission line from two
subregions of strong Lyman-alpha emission in a radio-quiet Lyman-alpha blob
(LAB). The blob under study is LAB1 (Steidel et al. 2000) at z ~ 3.1, and the
[OIII] detections are from the two Lyman break galaxies embedded in the blob
halo. The [OIII] measurements were made with LUCIFER on the 8.4m Large
Binocular Telescope and NIRSPEC on 10m Keck Telescope. Comparing the redshift
of the [OIII] measurements to Lyman-alpha redshifts from SAURON (Weijmans et
al. 2010) allows us to take a step towards understanding the kinematics of the
gas in the blob. Using both LUCIFER and NIRSPEC we find velocity offsets
between the [OIII] and Lyman-alpha redshifts that are modestly negative or
consistent with 0 km/s in both subregions studied (ranging from -72 +/- 42 --
+6 +/- 33 km/s). A negative offset means Lyman-alpha is blueshifted with
respect to [OIII], a positive offset then implies Lyman-alpha is redshifted
with respect to [OIII]. These results may imply that outflows are not primarily
responsible for Lyman alpha escape in this LAB, since outflows are generally
expected to produce a positive velocity offset (McLinden et al. 2011). In
addition, we present an [OIII] line flux upper limit on a third region of LAB1,
a region that is unassociated with any underlying galaxy. We find that the
[OIII] upper limit from the galaxy-unassociated region of the blob is at least
1.4 -- 2.5 times fainter than the [OIII] flux from one of the LBG-associated
regions and has an [OIII] to Lyman-alpha ratio measured at least 1.9 -- 3.4
times smaller than the same ratio measured from one of the LBGs.
