  We present a best-fit analysis on the single-parameter holographic dark
energy model characterized by the conformal-age-like length,
$L=\frac{1}{a^4(t)}\int_0^tdt' a^3(t') $. Based on the Union2 compilation of
557 supernova Ia data, the baryon acoustic oscillation results from the SDSS
DR7 and the cosmic microwave background radiation data from the WMAP7, we show
that the model gives the minimal $\chi^2_{min}=546.273$, which is comparable to
$\chi^2_{\Lambda{\rm CDM}}=544.616$ for the $\Lambda$CDM model. The single
parameter $d$ concerned in the model is found to be $d=0.232\pm 0.006\pm
0.009$. Since the fractional density of dark energy $\Omega_{de}\sim d^2a^2$ at
$a \ll 1$, the fraction of dark energy is naturally negligible in the early
universe, $\Omega_{de} \ll 1$ at $a \ll 1$. The resulting constraints on the
present fractional energy density of matter and the equation of state are
$\Omega_{m0}=0.286^{+0.019}_{-0.018}^{+0.032}_{-0.028}$ and
$w_{de0}=-1.240^{+0.027}_{-0.027}^{+0.045}_{-0.044}$ respectively. The model
leads to a slightly larger fraction of matter comparing to the $\Lambda$CDM
model. We also provide a systematic analysis on the cosmic evolutions of the
fractional energy density of dark energy, the equation of state of dark energy,
the deceleration parameter and the statefinder. It is noticed that the equation
of state crosses from $w_{de}>-1$ to $w_{de}<-1$, the universe transits from
decelerated expansion ($q>0$) to accelerated expansion ($q<0$) recently, and
the statefinder may serve as a sensitive diagnostic to distinguish the CHDE
model with the $\Lambda$CDM model.
