Hopes are high that Lim's recent purchase of a majority stake in the club will end years of financial struggles and restore Valencia's status as genuine challengers for silverware in Spain and Europe.
They last won La Liga under coach Rafa Benitez in 2004 and were losing Champions League finalists in 2000 and 2001.
Chan, Valencia's first female president, was one of several executives close to Lim appointed to the new board this week and she told the club's website (www.valenciacf.com) on Wednesday there was a "bright future" ahead.
She cautioned that Valencia will have to comply with Financial Fair Play (FFP) rules imposed by European governing body UEFA that are designed to prevent clubs spending more on players and wages than they earn.
"We will always have constraints, we will always have a challenge to work within the budget under the Financial Fair Play," Chan said.
"Success will not come overnight. We will have to work on it and we have to work together very united," she added.
"I believe, and I am very positive and very confident, that we all have a bright future and Valencia will do very well.
"We have a very young team so I think we need to keep encouraging them and motivating them and get them to play together as a team."
Valencia are without a win in their last three La Liga matches, losing the last two, and are fifth after 13 matches, nine points behind leaders Real Madrid.
Their next outing in the Spanish top flight is at 16th-placed Granada on Sunday.
(Writing by Iain Rogers, editing by Toby Davis)
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