  The first observation of open b production in ep collisions is reported. An
event sample containing muons and jets has been selected which is enriched in
semileptonic b quark decays. The visible cross section \sigma(ep -> b \bar{b}X
-> \mu X') for Q^2 < 1 GeV^2, 0.1 < y < 0.8 is measured to be
0.176+-0.016(stat.)+0.026-0.017(syst.) nb for the muons to be detected in the
range 35 deg < \theta^\mu < 130 deg and \pt^\mu > 2.0 GeV in the laboratory
frame. The expected visible cross section based on a NLO QCD calculation is
0.104+-0.017 nb. The cross sections for electroproduction with Q^2<1 GeV^2 and
photoproduction are derived from the data and found to be \sigma(ep-> e
b\bar{b}X) = 7.1+-0.6(stat.)+1.5-1.3(syst.) nb and \sigma(\gamma p-> b\bar{b}
X) = 111+-10(stat.)+23-20(syst.) at an average <W_{\gamma p}> \sim 180 GeV,
respectively.
