"have a high chance of" is correct and usable in written English.
You can use this phrase to express that there is a greater likelihood of something happening compared to other possibilities. For example: The new vaccine is believed to have a high chance of success in providing immunity against the virus.
Those polls, Mr. Carter said, "are quite unreliable," and have a high chance of being biased.
Those who do have a high chance of being denied or having their applications delayed.
Mammalian viruses having dsRNA-binding regions and GW/WG motifs appear to have a high chance of conferring RSS activity.
People with epilepsy (PWE) have a high chance of experiencing depression and anxiety disorders over their lifetime.
If they donate enough money to party funds, they have a high chance of becoming peers of the realm.
Railway point systems are highly reliable systems the failure of which could lead to significant system delay and have a high chance of causing a fatal accident.
— that would have a high chance of falling in value, at the request of a hedge fund client who wanted to bet against it.
But it is another matter if you have a high chance of being snatched at gunpoint by rebel groups that are supposed to protect you.
Use of one "potentially accessible" vein on Hamm's right hand "would have a high chance of rupturing the vein and being unsuccessful," he added in a written statement Harcourt filed with the court.
You have a high chance of being raped, sexually harassed or sexually abused, and a very low chance that any perpetrator gets convicted, and you'll be told you deserved it anyway because of what you wore or where you went.
Hale's solicitor advised her she had a very strong case of discrimination under the Equality Act 2010 and would have a high chance of success in a county court, but this would probably come with a confidentiality clause.
