  We present evidence for unusually strong Halpha emission in galaxies with
spectroscopic redshifts in the range of 3.8<z<5.0, over the Great Observatories
Origins Deep Survey (GOODS) fields. Among 74 galaxies detected in the Spitzer
IRAC 3.6 and 4.5um bands, more than 70% of the galaxies show clear excess at
3.6um compared to the expected flux density from stellar continuum only. We
provide evidence that this 3.6um excess is due to Halpha emission redshifted
into the 3.6um band, and classify these 3.6um excess galaxies to be Halpha
emitter (HAE) candidates. The selection of HAE candidates using an excess in
broad-band filters is sensitive to objects whose rest-frame H$\alpha$
equivalent width is larger than 350A, star formation rates of 20-500 Msun/yr.
The Halpha-to-UV luminosity ratio of HAEs is on average larger than that of
local starbursts. Possible reasons for such strong Halpha emission in these
galaxies include different dust extinction properties, young stellar population
age, continuous star formation history, low metallicity, and top-heavy stellar
initial mass function. Although the correlation between UV slope beta and
L(Ha)/L(UV) raises the possibility that HAEs prefer a dust extinction curve
which is steeper in the UV, the most dominant factor that results in strong
Halpha emission appears to be star formation history. The Halpha equivalent
widths of HAEs are large despite their relatively old stellar population ages
constrained by SED fitting, suggesting that at least 60% of HAEs produce stars
at a constant rate. Under the assumption that the cold gas supply is sustained,
HAEs are able to produce ~50% of the observed stellar mass density at z~3 that
is caught in massive (M*>10^11 Msun) galaxies. This 'strong Halpha phase' of
star formation plays a dominant role in early galaxy growth, being a feasible
progenitors of massive red galaxies at lower redshifts.
