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We report the first X-ray detection of 113 Lyman-alpha emitters at redshift z~ 4.5. Only one source (J033127.2-274247) is detected in the Extended ChandraDeep Field South (ECDF-S) X-ray data, and has been spectroscopically confirmedas a z = 4.48 quasar with $L_X = 4.2\times 10^{44}$ erg/s. The single detectiongives a Lyman-alpha quasar density consistent with the X-ray luminosityfunction of quasars. The coadded counts of 22 Lyman-alpha emitters (LAEs) inthe central Chandra Deep Field South (CDF-S) region yields a S/N=2.4 (p=99.83%)detection at soft band, with an effective exposure time of ~36 Ms. Furtheranalysis of the equivalent width (EW) distribution shows that all the signalcomes from 12 LAE candidates with EW_rest < 400 \AA, and 2 of them contributeabout half of the signal. Following-up spectroscopic observations show that thetwo are a low-redshift emission line galaxy and a Lyman break galaxy at z =4.4. Excluding these two and combined with ECDF-S data, we derive a 3-sigmaupper limit on the average luminosity of $L_{0.5-2 keV}$ $<$ 2.4 $\times10^{42}$ ergs/s for z ~ 4.5 LAEs. If the average X-ray emission is due to starformation, it corresponds to a star-formation rate (SFR) of < 180--530 M$_\sun$per yr. We use this SFR_X as an upper limit of the unobscured SFR to constrainthe escape fraction of Lyman-alpha photons, and find a lower limit of f_esc >3-10%. However, our upper limit on the SFR_X is ~7 times larger than the upperlimit on SFR_X on z ~ 3.1 LAEs in the same field, and at least 30 times higherthan the SFR estimated from Lyman-alpha emission. From the average X-ray toLyman-alpha line ratio, we estimate that fewer than 3.2% (6.3%) of our LAEscould be high redshift type 1 (type 2) AGNs, and those hidden AGNs likely showlow rest frame EWs.

X-ray properties of the z ~ 4.5 Lyman-alpha Emitters in the Chandra Deep Field South Region