Being given a chance， she immediately jumped at it.

不可以。being为be的现在分词形式。being 既可以是谓语动词，也可以是非谓语动词。作为谓语动词，其用法比较简单，主要用于构成进行时态(含被动语态的进行时态)；作为非谓语动词，其用法则比较复杂，可用于引出短语构成主语、宾语、宾语补足语、定语、状语等。2.1）现在分词being 用作谓语动词1. being为助动词时的用法当being为助动词时，用作谓语动词动词的being主要与过去分词连用，构成被动语态。如：I'm always being criticized. 我总是挨批。He is being interviewed now. 他现在正在接受面试。He is being met at the station tonight. 今晚有人去车站迎接他。2. being为连系动词时的用法当being为连系动词时，用作谓语动词动词的being主要与形容词连用，表示临时特征或暂时现象。如：You’re being stupid. 你真傻。You are not being very polite. 你可是不大客气呀。Your brother is being very annoying this evening. 你兄弟今晚很烦人。2.2）现在分词being 用作非谓语动词1. being为助动词时的用法(1) 作主语。如：Being lost can be a terrifying experience. 迷路可能是一种很可怕的经历。Being recognized wherever you go is the price you pay for being famous. 出名所付出的代价是不管你走到哪里，都会被人认出来。 (2) 作宾语。如：He can't stand being kept waiting. 让他等着，他可不干。 Do you like being stared at? 你愿意人家盯着你看吗? (3) 作宾语补足语。如：I saw him being taken away by the police. 我看到他正被警察带走。I found myself being drawn into another dreary argument. 我发现竟然身不由己又参与了一次无聊的争论。It’s interesting (for children) to see a house being built. (孩子们)看造房子是挺有趣的事。(4) 作定语。如：Did you see that boy being questioned by the police? 你看见那个男孩受到警察的盘问了吗? We are going to reduce the number of trees being cut down. 我们要减少砍伐的树的数量。(5) 作状语。如：Being given a chance, she immediately jumped at it. 给了她这个机会，她立刻抓住。 Being well taken care of, she recovered quickly. 她受到很好的照顾，身体恢复得很快。注：有时 being 可带有自己的逻辑主语(构成独立主格结构)。如：The question being settled, we went home. 问题解决之后，我们就回家了。 2. being为连系动词时的用法(1) 作主语。如：Being tired often makes me short-tempered. 我一累就容易发脾气。Being deaf and dumb makes communication very difficult. 又聋又哑很难与人交往。 (2) 作宾语。如：I don’t like being in the office all day. 我不喜欢整天呆在办公室里。 You can be alone without being lonely. 你可以独处而不感到寂寞。 (3) 作宾语补足语。如：He said it to stop her being too proud. 他说这话是想要她不要太骄傲。I’m sorry to see you being so sad about it. 看到你对这事这样伤心，我很难过。She complains of the room being too small for her. 她埋怨房间太小了。(4) 作状语。如：Being anxious to please him, I bought him a nice present. 因为我想讨好他，我给他买了一件好礼物。Being unemployed, he hasn’t got much money. 由于他没有工作，他没有多少钱。(5) 用于独立主格结构。如：It being a holiday, all the shops were shut. 由于今天是假日，所有商店都关门了。 The weather being hot, we had to stay at home. 由于天气炎热，我们只好呆在家里。There being no further business, l declare the meeting closed. 没有再要讨论的事了，我宣布散会。 Other things being equal, Alice would marry Jim. 如果其他条件都一样的话，爱莉丝就会嫁给吉姆。2.3）使用现在分词being的两点特别说明1. 连系动词being不用作定语当being为连系动词时，非谓语动词结构being…可用作主语、宾语、宾语补足语、状语等，但是不能用作定语。遇此情况，可考虑改用定语从句。如：凡10点钟以后仍在外面的人将被逮捕。误：Anyone being outside after ten o’clock will be arrested. 正：Anyone who is outside after ten o’clock will be arrested.2. 助动词being可以用作定语当being为助动词时，非谓语动词结构being…可用作主语、宾语、宾语补足语、状语等，也可用作定语。如：The house being built is our new library. 正在建的房子是我们的新图书馆。That picture of the children being talked to by the Prime Minister is wonderful. 那张小孩子们正在聆听首相谈话的照片照得非常好。

不能换成by,因为这里是被动语态，现在分词短语做条件状语。这已经一语中的地解决了你的问题了，这里面牵涉到的语法知识就多了，被动语态和非谓语动词做状语是这个句子的语法关键点。