We present the first good evidence for exocomet transits of a host star in continuum light in data from the Kepler  mission .
The Kepler star in question , KIC 3542116 , is of spectral type F2V and is quite bright at K _ { p } = 10 .
The transits have a distinct asymmetric shape with a steeper ingress and slower egress that can be ascribed to objects with a trailing dust tail passing over the stellar disk .
There are three deeper transits with depths of \simeq 0.1 \% that last for about a day , and three that are several times more shallow and of shorter duration .
The transits were found via an exhaustive visual search of the entire Kepler photometric data set , which we describe in some detail .
We review the methods we use to validate the Kepler data showing the comet transits , and rule out instrumental artefacts as sources of the signals .
We fit the transits with a simple dust-tail model , and find that a transverse comet speed of \sim 35-50 km s ^ { -1 } and a minimum amount of dust present in the tail of \sim 10 ^ { 16 } g are required to explain the larger transits .
For a dust replenishment time of \sim 10 days , and a comet lifetime of only \sim 300 days , this implies a total cometary mass of \gtrsim 3 \times 10 ^ { 17 } g , or about the mass of Halley ’ s comet .
We also discuss the number of comets and orbital geometry that would be necessary to explain the six transits detected over the four years of Kepler prime-field observations .
Finally , we also report the discovery of a single comet-shaped transit in KIC 11084727 with very similar transit and host-star properties .