Chronotype is a characteristic of a person in a certain point of one's lifetime and it slowly changes with age. Adolescents start to go to bed later while schools impose early starting hours, which may become a problem for students who are unable to adapt their circadian rhythm. The aim of this study was to determine if differences in school starting times affect the students' chronotype, school success, or daytime sleepiness. We tested a total of 1020 students from four high schools in Osijek, Croatia. The students had alternating school shifts (school starting hours 7 AM or 13 PM and 8 AM or 14 PM, every other week, alternatively, respectively). The participants were tested using the Epworth Sleepiness Scale and the Morningness--Eveningness Questionnaire. Earlier chronotypes were characteristic of the students starting school earlier, but without significant difference in daytime sleepiness in comparison with those starting school later. Differences were also found between different age and gender groups, female and older students having earlier chronotypes. Students going to school earlier showed better school success than the latter. In conclusion, the study shows that students starting school earlier also have earlier chronotypes, which might be consequence of the adaptation to one hour earlier school starting time.