  Despite the intense activity in the year since the discovery of
superconductivity in MgB2, key parameters, in particular the upper and lower
critical fields Hc2 and Hc1 and their anisotropies, are not well-established,
largely because of the difficulty of growing MgB2 crystals. Attempts have been
made to deduce these parameters from experiments on polycrystalline material,
but they have substantial uncertainties. Hc2 is particularly important for
applications, as it is the field which quenches bulk super-conductivity. In
terms of understanding MgB2, it is now clear that the conventional
electron-phonon interaction is strong enough to account for the high transition
temperature Tc, but the consequences of the double super-conducting gap for the
anisotropy and its dependence on temperature, are uncertain. Here we describe
detailed direct measurements of Hc1(T) and Hc2(T) for the two principal
crystallographic directions in a clean single crystal of MgB2. For fields in
the c-direction, $\mu_0 H^c_{c1}(0)$ = $0.28 +- 0.01T$ and $\mu_0 H^c_{c2}(0)$
is $3 +- 0.5T$; this ratio of critical fields is rather low and implies that
MgB2 is only just a Type II super-conductor. The anisotropies of both critical
fields are close to 2.
