  We present the first limits on the Epoch of Reionization (EoR) 21-cm HI power
spectra, in the redshift range $z=7.9-10.6$, using the Low-Frequency Array
(LOFAR) High-Band Antenna (HBA). In total 13\,h of data were used from
observations centred on the North Celestial Pole (NCP). After subtraction of
the sky model and the noise bias, we detect a non-zero $\Delta^2_{\rm I} = (56
\pm 13 {\rm mK})^2$ (1-$\sigma$) excess variance and a best 2-$\sigma$ upper
limit of $\Delta^2_{\rm 21} < (79.6 {\rm mK})^2$ at $k=0.053$$h$cMpc$^{-1}$ in
the range $z=$9.6-10.6. The excess variance decreases when optimizing the
smoothness of the direction- and frequency-dependent gain calibration, and with
increasing the completeness of the sky model. It is likely caused by (i)
residual side-lobe noise on calibration baselines, (ii) leverage due to
non-linear effects, (iii) noise and ionosphere-induced gain errors, or a
combination thereof. Further analyses of the excess variance will be discussed
in forthcoming publications.
