We present deep optical and X-ray follow-up observations of the candidate radio-quiet MSP1FGL J1311.7-3429. The source was already known as an unidentified EGRET source (3EG J1314-3431, EGR J1314-3417), hence its nature has remained uncertain for the past two decades. Very recently, Romani (2012) found large-amplitude quasi-sinusoidal optical modulation with a 1.56 hr (5626 s) period, suggesting that the source could be another radio-quiet millisecond pulsar (MSP) after 1FGL J2339.7-0531. We also detected a quasi-sinusoidal optical modulation of m ~2 mag with a period of ~1.5 hr in the Rc, r' and g bands.

Moreover, we found that the amplitude of the modulation and peak intensity changed by ~1 mag and ~0.5 mag respectively, over our total six nights of observations from 2012 March and May. Combined with Swift UVOT data, the optical-UV spectrum is consistent with a blackbody temperature, kT ~ 1 eV, and the emission volume radius R_bb ~ 1.5x10^4 d_kpc km (d_kpc is the distance to the source in units of 1 kpc).

In contrast, deep Suzaku observations conducted in 2009 and 2011 revealed strong X-ray flares with a light curve characterized with a power spectrum density of P(f) propto f^(-2.0+-0.4), but the folded X-ray light curves suggest an orbital modulation also in X-rays. The physical origin of flaring X-ray and optical variability remains an open question and has never been observed in another radio-quiet MSP candidate 1FGL J2339.7-0531.