If the TESLA e+e- linear collider is constructed next to an existing
high energy proton storage ring, an electron-proton collider option for
this future facility could become attractive. In this talk the version of
TESLA vs. HERA-p with a center-of-mass energy of about 1 TeV (250 GeV(e-)*1000GeV(p))
is discussed. Basic machine parameters, achievable luminosity (several
10^30cm^-2s^-1) and possibilities for performance improvements (flat beams,
travelling focus, cooling) are presented.