  We present a multi-epoch Hubble Space Telescope (HST) study of stellar proper
motions (PMs) for four fields along the Orphan Stream. We determine absolute
PMs of several individual stars per target field using established techniques
that utilize distant background galaxies to define a stationary reference
frame. Five Orphan Stream stars are identified in one of the four fields based
on combined color-magnitude and PM information. The average PM is consistent
with the existing model of the Orphan stream by Newberg et al. In addition to
the Orphan stream stars, we detect stars that likely belong to other stellar
streams. To identify which stellar streams these stars belong to, we examine
the 2-d bulk motion of each group of stars on the sky by subtracting the PM
contribution of the solar motion (which is a function of position on the sky
and distance) from the observed PMs, and comparing the vector of net motion
with the spatial extent of known stellar streams. By doing this, we identify
candidate stars in the Sagittarius and Lethe streams, and a newly-found stellar
stream at a distance of ~17 kpc, which we tentatively name the "Parallel
stream". Together with our Sagittarius stream study (Sohn et al., 2015, ApJ,
803, 56), this work demonstrates that even in the Gaia era, HST will continue
to be advantageous in measuring PMs of old stellar populations on a
star-by-star basis, especially for distances beyond ~10 kpc.
