Consider the history of venezuela. in this context, why might the people of venezuela have supported a leader such as chavez

Because he was highly nationalistic and united the people of Venezuela when the took power. He spoke against foreign aggression and  this fact made him nationalize the oil that was own by American firms  (which he perceived as foreign economic aggression that only made his citizens poorer) and used the revenue to rebuild the country. It is mainly due to this fact that he became unpopular with the US.