▲同意刘老师的分析。on the chance是个习语，用于表示希望或推测，意思是“也许会（能）”“希望会（能）”，其后可接 of doing sth 或 that 从句（that可以省略），在含义上与 in the hope of doing sth 以及 in the hope that相似。如：
1. on the chance of doing sth
We went to the cinema on the chance of seeing him there. 我们去电影院希望在那儿能见到他。
I’ll return to the station on the chance of meeting his brother. 我将回到车站，期望遇到他的兄弟。
People will gather by hundreds outside a police court on the chance of catching a glimpse of the criminal. 数以百计的人聚在警署外希望看一眼罪犯。
2. on the chance (that)…
I came on the chance that I might find you at home. 我来这里就是希望能在家里找到你。
I offer the information on the chance that it may prove useful. 我提供这个信息是希望它有所作用。
▲Straitford’s briefs don’t sound like the usual Washington back-and-forthing, whereby agencies avoid dramatic declarations on the chance they might be wrong.
(1) 句中 the chance 和 they might be wrong 是什么关系？（是同位语关系吗？可是同位语从句中that不能省略。）

——是同位关系，引导同位语的 that 有时也可以省略的。如以下各句均摘自词典和语法著作：
I had a kind of feeling this might happen. 我隐约感到这事可能发生。
I had no idea you were such an actor. 我不知道你是一位这样出色的演员。
There was a risk the brain might be starved of oxygen. 大脑可能有缺氧的危险。
He gabbed his suitcase and gave the impression he was boarding the Tokyo plane. 他拿起了手提箱，给人的印象是他要登上飞往东京的飞机了。
(2) on the chance 在句中做什么成分？（状语还是declarations的定语还是其他？）

——感觉将其分析为状语比较好（表示原因），其实从本句来看，完全可以在 on the chance 前面加一个逗号。